SHELLINGS AND SHEDDINGS INDUCED BY COLLAPSES
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10436839" target="_blank" >RIV/00216208:11320/21:10436839 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=O9torzNYIx" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=O9torzNYIx</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/19M1290826" target="_blank" >10.1137/19M1290826</a>
Alternative languages
Result language
angličtina
Original language name
SHELLINGS AND SHEDDINGS INDUCED BY COLLAPSES
Original language description
We say that a pure simplicial complex K of dimension d satisfies the removal-collapsibility condition if K is either empty or K becomes collapsible after removing (beta) over tilde (d)(K; Z(2)) facets, where (beta) over tilde (d)(K; Z(2)) denotes the dth reduced Betti number. In this paper, we show that if the link of each face of a pure simplicial complex K (including the link of the empty face which is the whole K) satisfies the removal-collapsibility condition, then the second barycentric subdivision of 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 K is connected and K becomes simplicially collapsible after removing (chi) over tilde (K) facets, where (chi) over tilde (K) denotes the reduced Euler characteristic, then the second barycentric subdivision of 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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ19-04113Y" target="_blank" >GJ19-04113Y: Advanced tools in combinatorics, topology and related areas</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Discrete Mathematics
ISSN
0895-4801
e-ISSN
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Volume of the periodical
35
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
25
Pages from-to
1978-2002
UT code for WoS article
000703464500024
EID of the result in the Scopus database
2-s2.0-85115233075