{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,10]],"date-time":"2025-05-10T04:11:13Z","timestamp":1746850273864,"version":"3.40.5"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T00:00:00Z","timestamp":1742342400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T00:00:00Z","timestamp":1742342400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s00454-025-00729-2","type":"journal-article","created":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T16:43:53Z","timestamp":1742402633000},"page":"896-918","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Morse Shellings Out of Discrete Morse Functions"],"prefix":"10.1007","volume":"73","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0496-7118","authenticated-orcid":false,"given":"Jean-Yves","family":"Welschinger","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,19]]},"reference":[{"issue":"3","key":"729_CR1","doi-asserted-by":"publisher","first-page":"608","DOI":"10.1007\/s00454-019-00137-3","volume":"64","author":"K Adiprasito","year":"2020","unstructured":"Adiprasito, K., Benedetti, B.: Barycentric subdivisions of convex complexes are collapsible. Discrete Comput. Geom. 64(3), 608\u2013626 (2020)","journal-title":"Discrete Comput. Geom."},{"issue":"1","key":"729_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00493-016-3149-8","volume":"37","author":"KA Adiprasito","year":"2017","unstructured":"Adiprasito, K.A., Benedetti, B.: Subdivisions, shellability, and collapsibility of products. Combinatorica 37(1), 1\u201330 (2017)","journal-title":"Combinatorica"},{"issue":"2","key":"729_CR3","first-page":"335","volume":"16","author":"B Benedetti","year":"2016","unstructured":"Benedetti, B.: Smoothing discrete Morse theory. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 16(2), 335\u2013368 (2016)","journal-title":"Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)"},{"issue":"12","key":"729_CR4","doi-asserted-by":"publisher","first-page":"6631","DOI":"10.1090\/S0002-9947-2012-05614-5","volume":"364","author":"B Benedetti","year":"2012","unstructured":"Benedetti, B.: Discrete Morse theory for manifolds with boundary. Trans. Am. Math. Soc. 364(12), 6631\u20136670 (2012)","journal-title":"Trans. Am. Math. Soc."},{"issue":"3","key":"729_CR5","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/0097-3165(81)90058-3","volume":"31","author":"LJ Billera","year":"1981","unstructured":"Billera, L.J., Lee, C.W.: A proof of the sufficiency of McMullen\u2019s conditions for $$f$$-vectors of simplicial convex polytopes. J. Combin. Theory Ser. A 31(3), 237\u2013255 (1981)","journal-title":"J. Combin. Theory Ser. A"},{"issue":"1","key":"729_CR6","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1090\/S0002-9947-1980-0570784-2","volume":"260","author":"A Bj\u00f6rner","year":"1980","unstructured":"Bj\u00f6rner, A.: Shellable and Cohen\u2013Macaulay partially ordered sets. Trans. Am. Math. Soc. 260(1), 159\u2013183 (1980)","journal-title":"Trans. Am. Math. Soc."},{"issue":"197\u2013205","key":"729_CR7","first-page":"1971","volume":"29","author":"H Bruggesser","year":"1972","unstructured":"Bruggesser, H., Mani, P.: Shellable decompositions of cells and spheres. Math. Scand. 29(197\u2013205), 1971 (1972)","journal-title":"Math. Scand."},{"issue":"1","key":"729_CR8","doi-asserted-by":"publisher","first-page":"83","DOI":"10.2307\/1971245","volume":"110","author":"JW Cannon","year":"1979","unstructured":"Cannon, J.W.: Shrinking cell-like decompositions of manifolds. Codimension three. Ann. Math. (2) 110(1), 83\u2013112 (1979)","journal-title":"Ann. Math. (2)"},{"issue":"3","key":"729_CR9","doi-asserted-by":"publisher","first-page":"343","DOI":"10.5802\/alco.38","volume":"2","author":"G Codenotti","year":"2019","unstructured":"Codenotti, G., Katth\u00e4n, L., Sanyal, R.: On $$f$$- and $$h$$-vectors of relative simplicial complexes. Algebr. Combin. 2(3), 343\u2013353 (2019)","journal-title":"Algebr. Combin."},{"key":"729_CR10","unstructured":"Edwards, R.D.: The topology of manifolds and cell-like maps. In: Proceedings of the International Congress of Mathematicians (Helsinki, 1978), pp. 111\u2013127. Acad. Sci. Fennica, Helsinki (1980)"},{"issue":"1","key":"729_CR11","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1006\/aima.1997.1650","volume":"134","author":"R Forman","year":"1998","unstructured":"Forman, R.: Morse theory for cell complexes. Adv. Math. 134(1), 90\u2013145 (1998)","journal-title":"Adv. Math."},{"key":"729_CR12","unstructured":"Forman, R.: A user\u2019s guide to discrete Morse theory. S\u00e9m. Lothar. Combin. 48, B48c (2002)"},{"key":"729_CR13","unstructured":"Freedman, M.H., Quinn, F.: Topology of 4-manifolds. Princeton Mathematical Series, vol. 39. Princeton University Press, Princeton (1990)"},{"key":"729_CR14","doi-asserted-by":"crossref","unstructured":"Fulton, W.: Introduction to Toric Varieties, Volume 131 of Annals of Mathematics Studies, The William H. Roever Lectures in Geometry. Princeton University Press, Princeton (1993)","DOI":"10.1515\/9781400882526"},{"issue":"2","key":"729_CR15","first-page":"229","volume":"9","author":"E Gallais","year":"2010","unstructured":"Gallais, E.: Combinatorial realization of the Thom\u2013Smale complex via discrete Morse theory. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 9(2), 229\u2013252 (2010)","journal-title":"Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)"},{"issue":"1","key":"729_CR16","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/s002090000129","volume":"235","author":"M Hachimori","year":"2000","unstructured":"Hachimori, M., Ziegler, G.M.: Decompositions of simplicial balls and spheres with knots consisting of few edges. Math. Z. 235(1), 159\u2013171 (2000)","journal-title":"Math. Z."},{"key":"729_CR17","doi-asserted-by":"crossref","unstructured":"Kirby, R.C., Siebenmann, L.C.: Foundational essays on topological manifolds, smoothings, and triangulations. Annals of Mathematics Studies, No. 88. Princeton University Press, Princeton; University of Tokyo Press, Tokyo (1977). With notes by John Milnor and Michael Atiyah","DOI":"10.1515\/9781400881505"},{"key":"729_CR18","doi-asserted-by":"crossref","unstructured":"Kozlov, D.: Combinatorial algebraic topology. Algorithms and Computation in Mathematics, vol. 21. Springer, Berlin (2008)","DOI":"10.1007\/978-3-540-71962-5"},{"issue":"6","key":"729_CR19","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1016\/S0195-6698(13)80103-5","volume":"12","author":"WBR Lickorish","year":"1991","unstructured":"Lickorish, W.B.R.: Unshellable triangulations of spheres. Eur. J. Combin. 12(6), 527\u2013530 (1991)","journal-title":"Eur. J. Combin."},{"key":"729_CR20","doi-asserted-by":"crossref","unstructured":"Lickorish, W.B.R.: Simplicial moves on complexes and manifolds. In: Proceedings of the Kirbyfest (Berkeley, CA, 1998), Volume\u00a02 of Geom. Topol. Monogr., pp. 299\u2013320. Geom. Topol. Publ., Coventry (1999)","DOI":"10.2140\/gtm.1999.2.299"},{"key":"729_CR21","doi-asserted-by":"publisher","DOI":"10.1515\/9781400878055","volume-title":"Lectures on the $$h$$-Cobordism Theorem","author":"J Milnor","year":"1965","unstructured":"Milnor, J.: Lectures on the $$h$$-Cobordism Theorem. Notes by L. Siebenmann and J. Sondow. Princeton University Press, Princeton (1965)"},{"key":"729_CR22","unstructured":"Morse, M.: The calculus of variations in the large, Volume\u00a018 of American Mathematical Society Colloquium Publications. American Mathematical Society, Providence (1996). Reprint of the 1932 original"},{"key":"729_CR23","volume-title":"Elements of Algebraic Topology","author":"JR Munkres","year":"1984","unstructured":"Munkres, J.R.: Elements of Algebraic Topology. Addison-Wesley Publishing Company, Menlo Park (1984)"},{"key":"729_CR24","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/s10711-009-9406-x","volume":"148","author":"F Quinn","year":"2010","unstructured":"Quinn, F.: A controlled-topology proof of the product structure theorem. Geom. Dedicata. 148, 303\u2013308 (2010)","journal-title":"Geom. Dedicata."},{"key":"729_CR25","unstructured":"Rourke, C.P., Sanderson, B.J.: Introduction to piecewise-linear topology. Springer Study Edition. Springer, Berlin, New York (1982). Reprint"},{"key":"729_CR26","unstructured":"Salepci, N., Welschinger, J.-Y.: Tilings, packings and expected Betti numbers in simplicial complexes. arXiv:1806.05084 (2018)"},{"key":"729_CR27","unstructured":"Salepci, N., Welschinger, J.-Y.: Morse shellings and compatible discrete Morse functions. arXiv:1910.13241 (2019)"},{"key":"729_CR28","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2024.109010","volume":"355","author":"N Salepci","year":"2024","unstructured":"Salepci, N., Welschinger, J.-Y.: Upper estimates for the expected Betti numbers of random subcomplexes. Topol. Appl. 355, 109010 (2024)","journal-title":"Topol. Appl."},{"issue":"74","key":"729_CR29","doi-asserted-by":"publisher","first-page":"391","DOI":"10.2307\/1970239","volume":"2","author":"S Smale","year":"1961","unstructured":"Smale, S.: Generalized Poincar\u00e9\u2019s conjecture in dimensions greater than four. Ann. Math. 2(74), 391\u2013406 (1961)","journal-title":"Ann. Math."},{"key":"729_CR30","unstructured":"Stanley, R.: Generalized $$H$$-vectors, intersection cohomology of toric varieties, and related results. In: Commutative Algebra and Combinatorics (Kyoto, 1985), Volume\u00a011 of Adv. Stud. Pure Math., pp. 187\u2013213. North-Holland, Amsterdam (1987)"},{"issue":"3","key":"729_CR31","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1016\/0001-8708(80)90050-X","volume":"35","author":"RP Stanley","year":"1980","unstructured":"Stanley, R.P.: The number of faces of a simplicial convex polytope. Adv. Math. 35(3), 236\u2013238 (1980)","journal-title":"Adv. Math."},{"issue":"4","key":"729_CR32","first-page":"805","volume":"5","author":"RP Stanley","year":"1992","unstructured":"Stanley, R.P.: Subdivisions and local $$h$$-vectors. J. Am. Math. Soc. 5(4), 805\u2013851 (1992)","journal-title":"J. Am. Math. Soc."},{"key":"729_CR33","unstructured":"Stanley, R.P.: Combinatorics and commutative algebra. Volume\u00a041 of Progress in Mathematics, 2nd edn. Birkh\u00e4user Boston, Inc., Boston (1996)"},{"issue":"2","key":"729_CR34","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1515\/advgeom-2023-0001","volume":"23","author":"J-Y Welschinger","year":"2023","unstructured":"Welschinger, J.-Y.: Shellable tilings on relative simplicial complexes and their $$h$$-vectors. Adv. Geom. 23(2), 191\u2013206 (2023)","journal-title":"Adv. Geom."},{"issue":"2","key":"729_CR35","doi-asserted-by":"publisher","first-page":"241","DOI":"10.4310\/HHA.2022.v24.n2.a11","volume":"24","author":"J-Y Welschinger","year":"2022","unstructured":"Welschinger, J.-Y.: Spectral sequences of a Morse shelling. Homol. Homotopy Appl. 24(2), 241\u2013254 (2022)","journal-title":"Homol. Homotopy Appl."},{"issue":"4","key":"729_CR36","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1112\/plms\/s2-45.1.243","volume":"45","author":"JHC Whitehead","year":"1939","unstructured":"Whitehead, J.H.C.: Simplicial spaces, nuclei and m-groups. Proc. Lond. Math. Soc. (2) 45(4), 243\u2013327 (1939)","journal-title":"Proc. Lond. Math. Soc. (2)"},{"issue":"41","key":"729_CR37","doi-asserted-by":"publisher","first-page":"809","DOI":"10.2307\/1968861","volume":"2","author":"JHC Whitehead","year":"1940","unstructured":"Whitehead, J.H.C.: On $$C^1$$-complexes. Ann. Math. 2(41), 809\u2013824 (1940)","journal-title":"Ann. Math."},{"key":"729_CR38","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-8431-1","volume-title":"Lectures on polytopes","author":"GM Ziegler","year":"1995","unstructured":"Ziegler, G.M.: Lectures on polytopes. Graduate Texts in Mathematics, vol. 152. Springer, New York (1995)"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-025-00729-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-025-00729-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-025-00729-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T18:49:34Z","timestamp":1746816574000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-025-00729-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,19]]},"references-count":38,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["729"],"URL":"https:\/\/doi.org\/10.1007\/s00454-025-00729-2","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2025,3,19]]},"assertion":[{"value":"5 June 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 February 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 March 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 March 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}