SHELLINGS AND SHEDDINGS INDUCED BY COLLAPSES

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

SHELLINGS AND SHEDDINGS INDUCED BY COLLAPSES

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

SHELLINGS AND SHEDDINGS INDUCED BY COLLAPSES

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ19-04113Y" target="_blank" >GJ19-04113Y: Pokročilé nástroje v kombinatorice, topologii a příbuzných oblastech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

—

Svazek periodika

35

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

25

Strana od-do

1978-2002

Kód UT WoS článku

000703464500024

EID výsledku v databázi Scopus

2-s2.0-85115233075