{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:46:33Z","timestamp":1740109593205,"version":"3.37.3"},"reference-count":65,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T00:00:00Z","timestamp":1714089600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T00:00:00Z","timestamp":1714089600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["TRR 109"],"award-info":[{"award-number":["TRR 109"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100015052","name":"Fondation de l\u2019Ecole Normale Superieure","doi-asserted-by":"publisher","award":["ENS-MHI Chair in Mathematics"],"award-info":[{"award-number":["ENS-MHI Chair in Mathematics"]}],"id":[{"id":"10.13039\/100015052","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-18-CE40-0033"],"award-info":[{"award-number":["ANR-18-CE40-0033"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2025,3]]},"DOI":"10.1007\/s00454-024-00640-2","type":"journal-article","created":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T15:01:58Z","timestamp":1714143718000},"page":"370-436","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Schwarzian Octahedron Recurrence (dSKP Equation) II: Geometric Systems"],"prefix":"10.1007","volume":"73","author":[{"given":"Niklas Christoph","family":"Affolter","sequence":"first","affiliation":[]},{"given":"B\u00e9atrice","family":"de Tili\u00e8re","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2004-2764","authenticated-orcid":false,"given":"Paul","family":"Melotti","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,26]]},"reference":[{"issue":"4","key":"640_CR1","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1155\/S1073792800000118","volume":"2000","author":"SI Agafonov","year":"2000","unstructured":"Agafonov, S.I., Bobenko, A.I.: Discrete $$z^\\gamma $$ and Painlev\u00e9 equations. Int. Math. Res. Not. 2000(4), 165\u2013193 (2000)","journal-title":"Int. Math. Res. Not."},{"issue":"8","key":"640_CR2","doi-asserted-by":"crossref","first-page":"3455","DOI":"10.1063\/1.1586966","volume":"44","author":"SI Agafonov","year":"2003","unstructured":"Agafonov, S.I., Bobenko, A.I.: Hexagonal circle patterns with constant intersection angles and discrete Painlev\u00e9 and Riccati equations. J. Math. Phys. 44(8), 3455\u20133469 (2003)","journal-title":"J. Math. Phys."},{"issue":"3","key":"640_CR3","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1007\/s00220-002-0762-8","volume":"233","author":"VE Adler","year":"2003","unstructured":"Adler, V.E., Bobenko, A.I., Suris, Y.B.: Classification of integrable equations on quad-graphs. The consistency approach. Commun. Math. Phys. 233(3), 513\u2013543 (2003)","journal-title":"Commun. Math. Phys."},{"issue":"2","key":"640_CR4","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/BF01085984","volume":"27","author":"VE Adler","year":"1993","unstructured":"Adler, V.E.: Recuttings of polygons. Funct. Anal. Appl. 27(2), 141\u2013143 (1993)","journal-title":"Funct. Anal. Appl."},{"key":"640_CR5","doi-asserted-by":"crossref","unstructured":"Affolter, N.C., de\u00a0Tili\u00e8re, B., Melotti, P.: The Schwarzian octahedron recurrence (dSKP equation) I: explicit solutions. Comb. Theory 3(2) (2023)","DOI":"10.5070\/C63261993"},{"key":"640_CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11005-021-01406-0","volume":"111","author":"NC Affolter","year":"2021","unstructured":"Affolter, N.C.: Miquel dynamics, Clifford lattices and the Dimer model. Lett. Math. Phys. 111, 1\u201323 (2021)","journal-title":"Lett. Math. Phys."},{"key":"640_CR7","unstructured":"Affolter, N.C.: Discrete Differential Geometry and Cluster Algebras via TCD Maps, (2023). PhD thesis, arXiv:2305.02212"},{"key":"640_CR8","doi-asserted-by":"crossref","unstructured":"Arnold, M., Fuchs, D., Izmestiev, I., Tabachnikov, S.: Cross-ratio dynamics on ideal polygons. Int. Math. Res. Not. 12 (2020)","DOI":"10.1093\/imrn\/rnaa289"},{"key":"640_CR9","unstructured":"Affolter, N., George, T., Ramassamy, S.: Integrable dynamics in projective geometry via dimers and triple crossing diagram maps on the cylinder (2023). Preprint. arXiv:2108.12692"},{"issue":"3","key":"640_CR10","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1215\/S0012-7094-03-11635-X","volume":"116","author":"AI Bobenko","year":"2003","unstructured":"Bobenko, A.I., Hoffmann, T.: Hexagonal circle patterns and integrable systems: patterns with constant angles. Duke Math. J. 116(3), 525\u2013566 (2003)","journal-title":"Duke Math. J."},{"issue":"9","key":"640_CR11","doi-asserted-by":"crossref","first-page":"4683","DOI":"10.1063\/1.532540","volume":"39","author":"LV Bogdanov","year":"1998","unstructured":"Bogdanov, L.V., Konopelchenko, B.G.: Analytic-bilinear approach to integrable hierarchies. I. Generalized KP hierarchy. J. Math. Phys. 39(9), 4683\u20134700 (1998)","journal-title":"J. Math. Phys."},{"issue":"9","key":"640_CR12","doi-asserted-by":"crossref","first-page":"4701","DOI":"10.1063\/1.532531","volume":"39","author":"LV Bogdanov","year":"1998","unstructured":"Bogdanov, L.V., Konopelchenko, B.G.: Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies. J. Math. Phys. 39(9), 4701\u20134728 (1998)","journal-title":"J. Math. Phys."},{"issue":"583","key":"640_CR13","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1515\/crll.2005.2005.583.117","volume":"2005","author":"AI Bobenko","year":"2005","unstructured":"Bobenko, A.I., Mercat, C., Suris, Y.B.: Linear and nonlinear theories of discrete analytic functions. Integrable structure and isomonodromic Green\u2019s function. Journal f\u00fcr die reine und angewandte Mathematik 2005(583), 117\u2013161 (2005)","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"issue":"475","key":"640_CR14","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1515\/crll.1996.475.187","volume":"1996","author":"AI Bobenko","year":"1996","unstructured":"Bobenko, A.I., Pinkall, U.: Discrete isothermic surfaces. Journal f\u00fcr die reine und angewandte Mathematik 1996(475), 187\u2013208 (1996)","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"key":"640_CR15","first-page":"3","volume-title":"Discrete Integrable Geometry and Physics, Chapter Discretization of Surfaces and Integrable Systems","author":"AI Bobenko","year":"1999","unstructured":"Bobenko, A.I., Pinkall, U.: Discrete Integrable Geometry and Physics, Chapter Discretization of Surfaces and Integrable Systems, pp. 3\u201358. Oxford University Press, Oxford (1999)"},{"issue":"11","key":"640_CR16","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1155\/S1073792802110075","volume":"2002","author":"AI Bobenko","year":"2002","unstructured":"Bobenko, A.I., Suris, Y.B.: Integrable systems on quad-graphs. Int. Math. Res. Not. 2002(11), 573\u2013611 (2002)","journal-title":"Int. Math. Res. Not."},{"key":"640_CR17","series-title":"Graduate Studies in Mathematics","volume-title":"Discrete Differential Geometry: Integrable Structure","author":"AI Bobenko","year":"2008","unstructured":"Bobenko, A.I., Suris, Y.B.: Discrete Differential Geometry: Integrable Structure. Graduate Studies in Mathematics, Birkh\u00e4user, Boston (2008)"},{"key":"640_CR18","unstructured":"Chelkak, D., Laslier, B., Russkikh, M.: Bipartite dimer model: perfect t-embeddings and Lorentz-minimal surfaces (2021). Preprint. arXiv:2109.06272"},{"issue":"5","key":"640_CR19","doi-asserted-by":"crossref","first-page":"1656","DOI":"10.1112\/plms.12516","volume":"126","author":"D Chelkak","year":"2023","unstructured":"Chelkak, D., Laslier, B., Russkikh, M.: Dimer model and holomorphic functions on t-embeddings of planar graphs. Proc. Lond. Math. Soc. 126(5), 1656\u20131739 (2023)","journal-title":"Proc. Lond. Math. Soc."},{"key":"640_CR20","volume-title":"Introduction to Geometry. Wiley Classics Library","author":"HSM Coxeter","year":"1989","unstructured":"Coxeter, H.S.M.: Introduction to Geometry. Wiley Classics Library, 2nd edn. Wiley, New York (1989)","edition":"2"},{"issue":"2","key":"640_CR21","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/0375-9601(91)90080-R","volume":"157","author":"IY Dorfman","year":"1991","unstructured":"Dorfman, I.Y., Nijhoff, F.W.: On a (2+1)-dimensional version of the Krichever-Novikov equation. Phys. Lett. A 157(2), 107\u2013112 (1991)","journal-title":"Phys. Lett. A"},{"issue":"1","key":"640_CR22","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1007\/s11075-022-01344-5","volume":"92","author":"A Doliwa","year":"2023","unstructured":"Doliwa, A., Siemaszko, A.: Integrability and geometry of the Wynn recurrence. Numer. Algorithms 92(1), 571\u2013596 (2023)","journal-title":"Numer. Algorithms"},{"issue":"2","key":"640_CR23","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1215\/S0012-7094-56-02332-8","volume":"23","author":"RJ Duffin","year":"1956","unstructured":"Duffin, R.J.: Basic properties of discrete analytic functions. Duke Math. J. 23(2), 335\u2013363 (1956)","journal-title":"Duke Math. J."},{"issue":"5","key":"640_CR24","doi-asserted-by":"crossref","first-page":"747","DOI":"10.24033\/asens.2201","volume":"46","author":"AB Goncharov","year":"2013","unstructured":"Goncharov, A.B., Kenyon, R.W.: Dimers and cluster integrable systems. Annales scientifiques de l\u2019\u00c9cole Normale Sup\u00e9rieure 46(5), 747\u2013813 (2013)","journal-title":"Annales scientifiques de l\u2019\u00c9cole Normale Sup\u00e9rieure"},{"issue":"2","key":"640_CR25","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1016\/j.aim.2011.02.018","volume":"227","author":"M Glick","year":"2011","unstructured":"Glick, M.: The pentagram map and Y-patterns. Adv. Math. 227(2), 1019\u20131045 (2011)","journal-title":"Adv. Math."},{"key":"640_CR26","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.geomphys.2014.07.029","volume":"87","author":"M Glick","year":"2015","unstructured":"Glick, M.: The Devron property. J. Geom. Phys. 87, 161\u2013189 (2015)","journal-title":"J. Geom. Phys."},{"issue":"9","key":"640_CR27","doi-asserted-by":"crossref","first-page":"2818","DOI":"10.1093\/imrn\/rny110","volume":"2020","author":"M Glick","year":"2018","unstructured":"Glick, M.: The limit point of the pentagram map. Int. Math. Res. Not. 2020(9), 2818\u20132831 (2018)","journal-title":"Int. Math. Res. Not."},{"issue":"4","key":"640_CR28","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1112\/plms\/pdw007","volume":"112","author":"M Glick","year":"2016","unstructured":"Glick, M., Pylyavskyy, P.: Y-meshes and generalized pentagram maps. Proc. Lond. Math. Soc. 112(4), 753\u2013797 (2016)","journal-title":"Proc. Lond. Math. Soc."},{"key":"640_CR29","doi-asserted-by":"crossref","first-page":"1825","DOI":"10.1103\/PhysRevLett.67.1825","volume":"67","author":"B Grammaticos","year":"1991","unstructured":"Grammaticos, B., Ramani, A., Papageorgiou, V.: Do integrable mappings have the Painlev\u00e9 property? Phys. Rev. Lett. 67, 1825\u20131828 (1991)","journal-title":"Phys. Rev. Lett."},{"key":"640_CR30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3934\/era.2012.19.1","volume":"19","author":"M Gekhtman","year":"2012","unstructured":"Gekhtman, M., Shapiro, M., Tabachnikov, S., Vainshtein, A.: Higher pentagram maps, weighted directed networks, and cluster dynamics. Electron. Res. Announc. 19, 1\u201317 (2012)","journal-title":"Electron. Res. Announc."},{"key":"640_CR31","first-page":"129","volume":"534","author":"U Hertrich-Jeromin","year":"2001","unstructured":"Hertrich-Jeromin, U., McIntosh, I., Norman, P., Pedit, F.: Periodic discrete conformal maps. Journal f\u00fcr die reine und angewandte Mathematik 534, 129\u2013153 (2001)","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"key":"640_CR32","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1103\/PhysRevLett.81.325","volume":"81","author":"J Hietarinta","year":"1998","unstructured":"Hietarinta, J., Viallet, C.: Singularity confinement and chaos in discrete systems. Phys. Rev. Lett. 81, 325\u2013328 (1998)","journal-title":"Phys. Rev. Lett."},{"key":"640_CR33","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1007\/s00220-016-2739-z","volume":"347","author":"R Inoue","year":"2015","unstructured":"Inoue, R., Lam, T., Pylyavskyy, P.: Toric networks, geometric R-matrices and generalized discrete Toda lattices. Commun. Math. Phys. 347, 799\u2013855 (2015)","journal-title":"Commun. Math. Phys."},{"issue":"4","key":"640_CR34","first-page":"861","volume":"32","author":"A Izosimov","year":"2022","unstructured":"Izosimov, A.: Dimers, networks, and cluster integrable systems. Geom. Funct. Anal. 32(4), 861\u2013880 (2022)","journal-title":"Geom. Funct. Anal."},{"issue":"2","key":"640_CR35","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s00029-023-00826-1","volume":"29","author":"A Izosimov","year":"2023","unstructured":"Izosimov, A.: Polygon recutting as a cluster integrable system. Selecta Mathematica 29(2), 21 (2023)","journal-title":"Selecta Mathematica"},{"key":"640_CR36","doi-asserted-by":"crossref","first-page":"1209","DOI":"10.1016\/0031-8914(61)90063-5","volume":"27","author":"PW Kasteleyn","year":"1961","unstructured":"Kasteleyn, P.W.: The statistics of dimers on a lattice: I. The number of dimer arrangements on a quadratic lattice. Physica 27, 1209\u20131225 (1961)","journal-title":"Physica"},{"key":"640_CR37","unstructured":"Kasteleyn, P.W.: Graph theory and crystal physics. In: Graph Theory and Theoretical Physics, pp. 43\u2013110. Academic Press, London (1967)"},{"issue":"2","key":"640_CR38","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s00222-002-0249-4","volume":"150","author":"RW Kenyon","year":"2002","unstructured":"Kenyon, R.W.: The Laplacian and Dirac operators on critical planar graphs. Inventiones mathematicae 150(2), 409\u2013439 (2002)","journal-title":"Inventiones mathematicae"},{"key":"640_CR39","unstructured":"Kenyon, R.W., Lam, W.Y., Ramassamy, S., Russkikh, M.: Dimers and Circle Patterns, 10 (2018). Preprint on arXiv:1810.05616"},{"issue":"29","key":"640_CR40","doi-asserted-by":"crossref","first-page":"6125","DOI":"10.1088\/0305-4470\/35\/29\/313","volume":"35","author":"BG Konopelchenko","year":"2002","unstructured":"Konopelchenko, B.G., Schief, W.K.: Menelaus\u2019 theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy. J. Phys. A: Math. Gen. 35(29), 6125\u20136144 (2002)","journal-title":"J. Phys. A: Math. Gen."},{"key":"640_CR41","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1088\/0305-4470\/36\/3\/313","volume":"36","author":"AD King","year":"2003","unstructured":"King, A.D., Schief, W.K.: Tetrahedra, octahedra and cubo-octahedra: integrable geometry of multi-ratios. J. Phys. A: Math. Gen. 36, 785 (2003)","journal-title":"J. Phys. A: Math. Gen."},{"issue":"3","key":"640_CR42","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1007\/s00208-013-0922-5","volume":"357","author":"B Khesin","year":"2013","unstructured":"Khesin, B., Soloviev, F.: Integrability of higher pentagram maps. Mathematische Annalen 357(3), 1005\u20131047 (2013)","journal-title":"Mathematische Annalen"},{"issue":"6","key":"640_CR43","doi-asserted-by":"crossref","first-page":"1808","DOI":"10.1093\/imrn\/rnw267","volume":"2018","author":"WY Lam","year":"2016","unstructured":"Lam, W.Y.: Discrete minimal surfaces: critical points of the area functional from integrable systems. Int. Math. Res. Not. 2018(6), 1808\u20131845 (2016)","journal-title":"Int. Math. Res. Not."},{"issue":"2","key":"640_CR44","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/s00332-012-9152-3","volume":"23","author":"G Mar\u00ed Beffa","year":"2013","unstructured":"Mar\u00ed Beffa, G.: On generalizations of the pentagram map: discretizations of AGD flows. J. Nonlinear Sci. 23(2), 303\u2013334 (2013)","journal-title":"J. Nonlinear Sci."},{"key":"640_CR45","unstructured":"Miquel, A.: Th\u00e9or\u00e8mes sur les intersections des cercles et des sph\u00e8res. J. Math. Pures Appl., pp. 517\u2013522 (1838)"},{"key":"640_CR46","first-page":"06","volume":"57","author":"C M\u00fcller","year":"2015","unstructured":"M\u00fcller, C.: Planar discrete isothermic nets of conical type. Beitr\u00e4ge zur Algebra und Geometrie \/ Contributions to Algebra and Geometry 57, 06 (2015)","journal-title":"Beitr\u00e4ge zur Algebra und Geometrie \/ Contributions to Algebra and Geometry"},{"issue":"1","key":"640_CR47","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/BF00994631","volume":"39","author":"F Nijhoff","year":"1995","unstructured":"Nijhoff, F., Capel, H.: The discrete Korteweg-de Vries equation. Acta Applicandae Mathematica 39(1), 133\u2013158 (1995)","journal-title":"Acta Applicandae Mathematica"},{"issue":"6","key":"640_CR48","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/0375-9601(84)90994-0","volume":"105","author":"FW Nijhoff","year":"1984","unstructured":"Nijhoff, F.W., Capel, H.W., Wiersma, G.L., Quispel, G.R.W.: B\u00e4cklund transformations and three-dimensional lattice equations. Phys. Lett. A 105(6), 267\u2013272 (1984)","journal-title":"Phys. Lett. A"},{"issue":"2","key":"640_CR49","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s00220-010-1075-y","volume":"299","author":"V Ovsienko","year":"2010","unstructured":"Ovsienko, V., Schwartz, R., Tabachnikov, S.: The pentagram map: a discrete integrable system. Commun. Math. Phys. 299(2), 409\u2013446 (2010)","journal-title":"Commun. Math. Phys."},{"issue":"3","key":"640_CR50","first-page":"813","volume":"2020","author":"S Ramassamy","year":"2018","unstructured":"Ramassamy, S.: Miquel dynamics for circle patterns. Int. Math. Res. Not. 2020(3), 813\u2013852 (2018)","journal-title":"Int. Math. Res. Not."},{"key":"640_CR51","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-17286-1","volume-title":"Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry","author":"J Richter-Gebert","year":"2011","unstructured":"Richter-Gebert, J.: Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry, Incorporated 1 Springer, Berlin (2011)","edition":"Incorporated 1"},{"issue":"1","key":"640_CR52","first-page":"71","volume":"1","author":"R Schwartz","year":"1992","unstructured":"Schwartz, R.: The pentagram map. Exp. Math. 1(1), 71\u201381 (1992)","journal-title":"Exp. Math."},{"issue":"2","key":"640_CR53","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1215\/S0012-7094-97-08611-7","volume":"86","author":"O Schramm","year":"1997","unstructured":"Schramm, O.: Circle patterns with the combinatorics of the square grid. Duke Math. J. 86(2), 347\u2013389 (1997)","journal-title":"Duke Math. J."},{"issue":"sup2","key":"640_CR54","doi-asserted-by":"crossref","first-page":"194","DOI":"10.2991\/jnmp.2003.10.s2.17","volume":"10","author":"WK Schief","year":"2003","unstructured":"Schief, W.K.: Lattice geometry of the discrete Darboux, KP, BKP and CKP equations. Menelaus\u2019 and Carnot\u2019s theorems. J. Nonlinear Math. Phys. 10(sup2), 194\u2013208 (2003)","journal-title":"J. Nonlinear Math. Phys."},{"key":"640_CR55","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s11784-008-0079-0","volume":"3","author":"R Schwartz","year":"2007","unstructured":"Schwartz, R.: Discrete monodromy, pentagrams, and the method of condensation. J. Fixed Point Theory Appl. 3, 379\u2013409 (2007)","journal-title":"J. Fixed Point Theory Appl."},{"key":"640_CR56","unstructured":"Schief, W.K.: Discrete Laplace-Darboux sequences, Menelaus\u2019 theorem and the pentagram map, (2009). Talk at workshop: Geometric Aspects of Discrete and Ultra-discrete Integrable Systems, Glasgow"},{"key":"640_CR57","doi-asserted-by":"crossref","unstructured":"Smirnov, S.: Discrete Complex Analysis and Probability, pp. 595\u2013621 (2010)","DOI":"10.1142\/9789814324359_0026"},{"key":"640_CR58","first-page":"06","volume":"162","author":"F Soloviev","year":"2011","unstructured":"Soloviev, F.: Integrability of the pentagram map. Duke Math. J. 162, 06 (2011)","journal-title":"Duke Math. J."},{"issue":"3","key":"640_CR59","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s10801-006-0039-y","volume":"25","author":"DE Speyer","year":"2007","unstructured":"Speyer, D.E.: Perfect matchings and the octahedron recurrence. J. Algebraic Comb. 25(3), 309\u2013348 (2007)","journal-title":"J. Algebraic Comb."},{"key":"640_CR60","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/S1874-5709(02)80013-0","volume-title":"Geometric Function Theory, Volume 1 of Handbook of Complex Analysis","author":"K Stephenson","year":"2002","unstructured":"Stephenson, K.: Chapter 11\u2013circle packing and discrete analytic function theory. In: K\u00fchnau, R. (ed.) Geometric Function Theory, Volume 1 of Handbook of Complex Analysis, pp. 333\u2013370. North-Holland, Amsterdam (2002)"},{"key":"640_CR61","unstructured":"Tabachnikov, S., Tsukerman, E.: On the discrete bicycle transformation. In: Proceedings of the Montevideo Dynamical Systems Congress 2012, Volume\u00a014 of Publicaciones Matem\u00e1ticas del Uruguay, pp. 201\u2013220 (2013)"},{"key":"640_CR62","doi-asserted-by":"crossref","unstructured":"Vinberg, EB.: Geometry II: Spaces of Constant Curvature. Encyclopaedia of Mathematical Sciences. Springer, Berlin (1993)","DOI":"10.1007\/978-3-662-02901-5"},{"issue":"10","key":"640_CR63","doi-asserted-by":"crossref","first-page":"3460","DOI":"10.1017\/etds.2022.82","volume":"43","author":"MH Weinreich","year":"2023","unstructured":"Weinreich, M.H.: The algebraic dynamics of the pentagram map. Ergod. Theory Dyn. Syst. 43(10), 3460\u20133505 (2023)","journal-title":"Ergod. Theory Dyn. Syst."},{"issue":"3","key":"640_CR64","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1007\/BF02162562","volume":"8","author":"P Wynn","year":"1966","unstructured":"Wynn, P.: Upon systems of recursions which obtain among the quotients of the Pad\u00e9 table. Numerische Mathematik 8(3), 264\u2013269 (1966)","journal-title":"Numerische Mathematik"},{"key":"640_CR65","unstructured":"Yao, Z.: Glick\u2019s conjecture on the point of collapse of axis-aligned polygons under the pentagram maps (2014). Preprint arXiv:1410.7806"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-024-00640-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-024-00640-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-024-00640-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,17]],"date-time":"2025-02-17T23:53:13Z","timestamp":1739836393000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-024-00640-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,26]]},"references-count":65,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["640"],"URL":"https:\/\/doi.org\/10.1007\/s00454-024-00640-2","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2024,4,26]]},"assertion":[{"value":"23 January 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 November 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 March 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 April 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}