{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:45:21Z","timestamp":1787323521499,"version":"build-2736575974"},"reference-count":12,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-17-CE40-0033"],"award-info":[{"award-number":["ANR-17-CE40-0033"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001824","name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","doi-asserted-by":"publisher","award":["19-04113Y"],"award-info":[{"award-number":["19-04113Y"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008579","name":"P\u0159\u00edrodov\u011bdeck\u00e1 Fakulta, Univerzita Karlova","doi-asserted-by":"publisher","award":["UNCE\/SCI\/004"],"award-info":[{"award-number":["UNCE\/SCI\/004"]}],"id":[{"id":"10.13039\/100008579","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We say that a pure simplicial complex ${\\mathbf K}$ of dimension $d$ satisfies the removal-collapsibility condition if ${\\mathbf K}$ is either empty or ${\\mathbf K}$ becomes collapsible after removing $\\tilde \\beta_d ({\\mathbf K}; {\\mathbb Z}_2)$ facets, where $\\tilde \\beta_d ({\\mathbf K}; {\\mathbb Z}_2)$ denotes the $d$th reduced Betti number. In this paper, we show that if the link of each face of a pure simplicial complex ${\\mathbf K}$ (including the link of the empty face which is the whole ${\\mathbf K}$) satisfies the removal-collapsibility condition, then the second barycentric subdivision of ${\\mathbf K}$ is vertex decomposable and in particular shellable. This is a higher-dimensional generalization of a result of Hachimori, who proved that if the link of each vertex of a pure 2-dimensional simplicial complex ${\\mathbf K}$ is connected and ${\\mathbf K}$ becomes simplicially collapsible after removing $\\tilde{\\chi}({\\mathbf K})$ facets, where $\\tilde \\chi ({\\mathbf K})$ denotes the reduced Euler characteristic, then the second barycentric subdivision of ${\\mathbf K}$ is shellable. For the proof, we introduce a new variant of decomposability of a simplicial complex, stronger than vertex decomposability, which we call star decomposability. This notion may be of independent interest.<\/jats:p>","DOI":"10.1137\/19m1290826","type":"journal-article","created":{"date-parts":[[2021,9,2]],"date-time":"2021-09-02T12:47:21Z","timestamp":1630586841000},"page":"1978-2002","source":"Crossref","is-referenced-by-count":0,"title":["Shellings and Sheddings Induced by Collapses"],"prefix":"10.1137","volume":"35","author":[{"given":"Thomas","family":"Magnard","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Skotnica","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Tancer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,9,2]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-016-3149-8"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.37236\/3319"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1983-0690055-6"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1145\/3314024"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2006.10.023"},{"key":"atypb6","doi-asserted-by":"crossref","unstructured":"J. Herzog and Y. Takayama,\n                      Resolutions by mapping cones\n                      , Homology Homotopy Appl., 4 (2, part 2, 2002), pp. 277-294.","DOI":"10.4310\/HHA.2002.v4.n2.a13"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/BF02558464"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"D. Kozlov,\n                      Combinatorial Algebraic Topology\n                      , Algorithms and Computation in Mathematics 21, Springer-Verlag, Berlin, 2008.","DOI":"10.1007\/978-3-540-71962-5"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(13)80103-5"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1287\/moor.5.4.576"},{"key":"atypb11","unstructured":"C. P. Rourke and B. J. Sanderson,\n                      Introduction to Piecewise-Linear Topology\n                      , Springer Study Edition, Springer-Verlag, Berlin, 1982."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-45.1.243"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1290826","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:07:11Z","timestamp":1787321231000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1290826"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/19M1290826"],"URL":"https:\/\/doi.org\/10.1137\/19m1290826","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}