{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T10:36:18Z","timestamp":1762079778980},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,2,1]],"date-time":"2021-02-01T00:00:00Z","timestamp":1612137600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,2,1]],"date-time":"2021-02-01T00:00:00Z","timestamp":1612137600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s00493-020-4369-5","type":"journal-article","created":{"date-parts":[[2021,2,1]],"date-time":"2021-02-01T17:05:53Z","timestamp":1612199153000},"page":"407-423","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Persistent Graphs and Cyclic Polytope Triangulations"],"prefix":"10.1007","volume":"41","author":[{"given":"Vincent","family":"Froese","sequence":"first","affiliation":[]},{"given":"Malte","family":"Renken","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,2,1]]},"reference":[{"key":"4369_CR1","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1142\/S0218195993000038","volume":"3","author":"J Abello","year":"1993","unstructured":"J. Abello and \u00d6. Egecioglu: Visibility graphs of staircase polygons with uniform step length, International Journal of Computational Geometry & Applications 3 (1993), 27\u201337.","journal-title":"International Journal of Computational Geometry & Applications"},{"key":"4369_CR2","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/BF02570710","volume":"14","author":"J Abello","year":"1995","unstructured":"J. Abello, \u00d6. Egecioglu and K. Kumar: Visibility graphs of staircase polygons and the weak Bruhat order, I: from visibility graphs to maximal chains, Discrete & Computational Geometry 14 (1995), 331\u2013358.","journal-title":"Discrete & Computational Geometry"},{"key":"4369_CR3","unstructured":"S. Ameer, M. Gibson-Lopez, E. Krohn, S. Soderman and Q. Wang: Terrain visibility graphs: Persistence is not enough, in: 36th International Symposium on Computational Geometry (SoCG 2020), volume 164 of LIPIcs, 6 1\u20136:13, Schloss Dagstuhl \u2014 Leibniz-Zentrum f\u00fcr Informatik, 2020."},{"key":"4369_CR4","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s00454-001-0050-y","volume":"27","author":"M Azaola","year":"2002","unstructured":"M. Azaola and F. Santos: The number of triangulations of the cyclic polytope c(n,n \u2212 4), Discrete & Computational Geometry 27 (2002), 29\u201348.","journal-title":"Discrete & Computational Geometry"},{"key":"4369_CR5","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1007\/BF02764601","volume":"15","author":"M Breen","year":"1973","unstructured":"M. Breen: Primitive radon partitions for cyclic polytopes, Israel Journal of Mathematics 15 (1973), 156\u2013157.","journal-title":"Israel Journal of Mathematics"},{"key":"4369_CR6","unstructured":"P. Colley: Recognizing visibility graphs of unimonotone polygons, in: Proceedings of the Fourth Canadian Conference on Computational Geometry (CCCG 1992), 29\u201334, 1992."},{"key":"4369_CR7","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/0925-7721(93)90005-Q","volume":"3","author":"T K Dey","year":"1993","unstructured":"T. K. Dey: On counting triangulations in d dimensions, Computational Geometry 3 (1993), 315\u2013325.","journal-title":"Computational Geometry"},{"key":"4369_CR8","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1112\/S0025579300011633","volume":"43","author":"P H Edelman","year":"1996","unstructured":"P. H. Edelman and V. Reiner: The higher stasheff-tamari posets, Mathematika 43 (1996), 127\u2013154.","journal-title":"Mathematika"},{"key":"4369_CR9","first-page":"108","volume":"6","author":"W S Evans","year":"2015","unstructured":"W. S. Evans and N. Saeedi: On characterizing terrain visibility graphs, Journal of Computational Geometry 6 (2015), 108\u2013141.","journal-title":"Journal of Computational Geometry"},{"key":"4369_CR10","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/S0166-218X(00)00232-8","volume":"109","author":"S Felsner","year":"2001","unstructured":"S. Felsner and H. Weil: Sweeps, arrangements and signotopes, Discrete Applied Mathematics 109 (2001), 67\u201394.","journal-title":"Discrete Applied Mathematics"},{"key":"4369_CR11","doi-asserted-by":"publisher","unstructured":"V. Froese and M. Renken: A fast shortest path algorithm on terrain-like graphs, Discrete & Computational Geometry, https:\/\/doi.org\/10.1007\/s00454-020-00226-8, (2020).","DOI":"10.1007\/s00454-020-00226-8"},{"key":"4369_CR12","unstructured":"V. Froese and M. Renken: Advancing through terrains, 2019, arXiv:1904.08746."},{"key":"4369_CR13","doi-asserted-by":"crossref","unstructured":"D. Gale: Neighborly and cyclic polytopes, in: Convexity, volume 7 of Proceedings of Symposia in Pure Mathematics, AMS, 1963.","DOI":"10.1090\/pspum\/007\/0152944"},{"key":"4369_CR14","doi-asserted-by":"publisher","first-page":"2421","DOI":"10.1016\/j.physa.2011.02.031","volume":"390","author":"G Gutin","year":"2011","unstructured":"G. Gutin, T. Mansour and S. Severini: A characterization of horizontal visibility graphs and combinatorics on words, Physica A: Statistical Mechanics and its Applications 390 (2011), 2421\u20132428.","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"key":"4369_CR15","doi-asserted-by":"crossref","unstructured":"M. Joswig and L. Kastner: New counts for the number of triangulations of cyclic polytopes, in: Mathematical Software \u2014 ICMS 2018, volume 10931 of LNCS, 64\u2013271. Springer, 2018.","DOI":"10.1007\/978-3-319-96418-8_31"},{"key":"4369_CR16","first-page":"11","volume":"32","author":"M M Kapranov","year":"1991","unstructured":"M. M. Kapranov and V. A. Voevodsky: Combinatorial-geometric aspects of poly-category theory: pasting schemes and higher bruhat orders (list of results), Cahiers de Topologie et G\u00e9om\u00e9trie Diff\u00e9rentielle Cat\u00e9goriques 32 (1991), 11\u201327.","journal-title":"Cahiers de Topologie et G\u00e9om\u00e9trie Diff\u00e9rentielle Cat\u00e9goriques"},{"key":"4369_CR17","doi-asserted-by":"publisher","first-page":"4972","DOI":"10.1073\/pnas.0709247105","volume":"105","author":"L Lacasa","year":"2008","unstructured":"L. Lacasa, B. Luque, F. Ballesteros, J. Luque and J. C. Nu\u00f1o: From time series to complex networks: The visibility graph, Proceedings of the National Academy of Sciences 105 (2008), 4972\u20134975.","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"4369_CR18","doi-asserted-by":"crossref","unstructured":"J. A. De Loera, J\u00d6. Rambau and F. Santos: Triangulations: Structures for Algorithms and Applications, volume 25 of AACIM, Springer, 2010.","DOI":"10.1007\/978-3-642-12971-1"},{"key":"4369_CR19","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1112\/S0025579300002850","volume":"17","author":"P McMullen","year":"1970","unstructured":"P. McMullen: The maximum numbers of faces of a convex polytope, Mathematika 17 (1970), 179\u2013184.","journal-title":"Mathematika"},{"key":"4369_CR20","doi-asserted-by":"crossref","unstructured":"J. O\u2019Rourke and I. Streinu: Vertex-edge pseudo-visibility graphs: Characterization and recognition, in: Proceedings of the Thirteenth Annual Symposium on Computational Geometry (SoCG 1997), 119\u2013128, Association for Computing Machinery, 1997.","DOI":"10.1145\/262839.262915"},{"key":"4369_CR21","doi-asserted-by":"crossref","unstructured":"S. Oppermann and H. Thomas: Triangulations of cyclic polytopes, in: 24th International Conference on Formal Power Series and Algebraic Combinatorics (FP-SAC 2012), volume AR of DMTCS Proceedings, 619\u2013630, art. 55. Discrete Mathematics and Theoretical Computer Science, 2012.","DOI":"10.46298\/dmtcs.3068"},{"key":"4369_CR22","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1112\/S0025579300012055","volume":"44","author":"J Rambau","year":"1997","unstructured":"J. Rambau: Triangulations of cyclic polytopes and higher bruhat orders, Mathematika 44 (1997), 162\u2013194.","journal-title":"Mathematika"},{"key":"4369_CR23","doi-asserted-by":"crossref","unstructured":"J. Rambau and V. Reiner: A Survey of the Higher Stasheff-Tamari Orders, 351\u2013390, Springer, 2012.","DOI":"10.1007\/978-3-0348-0405-9_18"},{"key":"4369_CR24","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1023\/A:1022851226643","volume":"19","author":"H Thomas","year":"2002","unstructured":"H. Thomas: New combinatorial descriptions of the triangulations of cyclic polytopes and the second higher stasheff-tamari posets, Order 19 (2002), 327\u2013342.","journal-title":"Order"},{"key":"4369_CR25","doi-asserted-by":"crossref","unstructured":"G. M. Ziegler: Lectures on Polytopes, Springer, 1995.","DOI":"10.1007\/978-1-4613-8431-1"}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-020-4369-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00493-020-4369-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-020-4369-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T06:40:24Z","timestamp":1671000024000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00493-020-4369-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,1]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["4369"],"URL":"https:\/\/doi.org\/10.1007\/s00493-020-4369-5","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,1]]},"assertion":[{"value":"25 November 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 July 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 February 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}