H-vectors of simplicial complexes with Serre's conditions

Satoshi Murai, Naoki Terai

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We study h-vectors of simplicial complexes which satisfy Serre's condition (Sr). Let r be a positive integer. We say that a simplicial complex △ satisfies Serre's condition (Sr) if H̃ i(lk (F);K) = 0 for all F ∈ △ and for all i < min{r-1, dim lk (F)}, where lk (F) is the link of △ with respect to F and where H̃i(△;K) is the reduced homology groups of △ over a field K. The main result of this paper is that if △ satisfies Serre's condition (Sr) then (i) hk(△) is non-negative for k = 0, 1, . . ., r and (ii) ∑k≥r hk(△) is non-negative.

Original languageEnglish
Pages (from-to)1015-1028
Number of pages14
JournalMathematical Research Letters
Volume16
Issue number6
DOIs
Publication statusPublished - 2009 Jan 1
Externally publishedYes

Fingerprint

H-vector
Simplicial Complex
Non-negative
Homology Groups
Integer

Keywords

  • Graded Betti numbers
  • H-vectors
  • Serre's conditions
  • Stanley-Reisner rings

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

H-vectors of simplicial complexes with Serre's conditions. / Murai, Satoshi; Terai, Naoki.

In: Mathematical Research Letters, Vol. 16, No. 6, 01.01.2009, p. 1015-1028.

Research output: Contribution to journalArticle

@article{5c96b019648a4b56a375d6539b293f7c,
title = "H-vectors of simplicial complexes with Serre's conditions",
abstract = "We study h-vectors of simplicial complexes which satisfy Serre's condition (Sr). Let r be a positive integer. We say that a simplicial complex △ satisfies Serre's condition (Sr) if H̃ i(lk△ (F);K) = 0 for all F ∈ △ and for all i < min{r-1, dim lk△ (F)}, where lk△ (F) is the link of △ with respect to F and where H̃i(△;K) is the reduced homology groups of △ over a field K. The main result of this paper is that if △ satisfies Serre's condition (Sr) then (i) hk(△) is non-negative for k = 0, 1, . . ., r and (ii) ∑k≥r hk(△) is non-negative.",
keywords = "Graded Betti numbers, H-vectors, Serre's conditions, Stanley-Reisner rings",
author = "Satoshi Murai and Naoki Terai",
year = "2009",
month = "1",
day = "1",
doi = "10.4310/MRL.2009.v16.n6.a10",
language = "English",
volume = "16",
pages = "1015--1028",
journal = "Mathematical Research Letters",
issn = "1073-2780",
publisher = "International Press of Boston, Inc.",
number = "6",

}

TY - JOUR

T1 - H-vectors of simplicial complexes with Serre's conditions

AU - Murai, Satoshi

AU - Terai, Naoki

PY - 2009/1/1

Y1 - 2009/1/1

N2 - We study h-vectors of simplicial complexes which satisfy Serre's condition (Sr). Let r be a positive integer. We say that a simplicial complex △ satisfies Serre's condition (Sr) if H̃ i(lk△ (F);K) = 0 for all F ∈ △ and for all i < min{r-1, dim lk△ (F)}, where lk△ (F) is the link of △ with respect to F and where H̃i(△;K) is the reduced homology groups of △ over a field K. The main result of this paper is that if △ satisfies Serre's condition (Sr) then (i) hk(△) is non-negative for k = 0, 1, . . ., r and (ii) ∑k≥r hk(△) is non-negative.

AB - We study h-vectors of simplicial complexes which satisfy Serre's condition (Sr). Let r be a positive integer. We say that a simplicial complex △ satisfies Serre's condition (Sr) if H̃ i(lk△ (F);K) = 0 for all F ∈ △ and for all i < min{r-1, dim lk△ (F)}, where lk△ (F) is the link of △ with respect to F and where H̃i(△;K) is the reduced homology groups of △ over a field K. The main result of this paper is that if △ satisfies Serre's condition (Sr) then (i) hk(△) is non-negative for k = 0, 1, . . ., r and (ii) ∑k≥r hk(△) is non-negative.

KW - Graded Betti numbers

KW - H-vectors

KW - Serre's conditions

KW - Stanley-Reisner rings

UR - http://www.scopus.com/inward/record.url?scp=73849089456&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=73849089456&partnerID=8YFLogxK

U2 - 10.4310/MRL.2009.v16.n6.a10

DO - 10.4310/MRL.2009.v16.n6.a10

M3 - Article

AN - SCOPUS:73849089456

VL - 16

SP - 1015

EP - 1028

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 6

ER -