Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals

Karim A. Adiprasito; Anders Björner; Afshin Goodarzi

doi:https://doi.org/10.4171/JEMS/755

Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals

Karim A. Adiprasito, Anders Björner, Afshin Goodarzi

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

A numerical characterization is given of the h-triangles of sequentially Cohen- Macaulay simplicial complexes. This result determines the number of faces of various dimensions and codimensions that are possible in such a complex, generalizing the classical Macaulay-Stanley theorem to the nonpure case. Moreover, we characterize the possible Betti tables of componentwise linear ideals. A key tool in our investigation is a bijection between shifted multicomplexes of degree ≤d and shifted pure .d -1/-dimensional simplicial complexes.

Original language	English
Pages (from-to)	3851-3865
Number of pages	15
Journal	Journal of the European Mathematical Society
Volume	19
Issue number	12
DOIs	https://doi.org/10.4171/JEMS/755
State	Published - 2017

Keywords

Componentwise linear ideals
Face numbers
Sequential Cohen-Macaulayness
Simplicial complex
Stanley-Reisner rings

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

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https://doi.org/10.4171/JEMS/755

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title = "Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals",

abstract = "A numerical characterization is given of the h-triangles of sequentially Cohen- Macaulay simplicial complexes. This result determines the number of faces of various dimensions and codimensions that are possible in such a complex, generalizing the classical Macaulay-Stanley theorem to the nonpure case. Moreover, we characterize the possible Betti tables of componentwise linear ideals. A key tool in our investigation is a bijection between shifted multicomplexes of degree ≤d and shifted pure .d -1/-dimensional simplicial complexes.",

keywords = "Componentwise linear ideals, Face numbers, Sequential Cohen-Macaulayness, Simplicial complex, Stanley-Reisner rings",

author = "Adiprasito, {Karim A.} and Anders Bj{\"o}rner and Afshin Goodarzi",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society 2017.",

year = "2017",

doi = "https://doi.org/10.4171/JEMS/755",

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TY - JOUR

T1 - Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals

AU - Adiprasito, Karim A.

AU - Björner, Anders

AU - Goodarzi, Afshin

N1 - Publisher Copyright: © European Mathematical Society 2017.

PY - 2017

Y1 - 2017

N2 - A numerical characterization is given of the h-triangles of sequentially Cohen- Macaulay simplicial complexes. This result determines the number of faces of various dimensions and codimensions that are possible in such a complex, generalizing the classical Macaulay-Stanley theorem to the nonpure case. Moreover, we characterize the possible Betti tables of componentwise linear ideals. A key tool in our investigation is a bijection between shifted multicomplexes of degree ≤d and shifted pure .d -1/-dimensional simplicial complexes.

AB - A numerical characterization is given of the h-triangles of sequentially Cohen- Macaulay simplicial complexes. This result determines the number of faces of various dimensions and codimensions that are possible in such a complex, generalizing the classical Macaulay-Stanley theorem to the nonpure case. Moreover, we characterize the possible Betti tables of componentwise linear ideals. A key tool in our investigation is a bijection between shifted multicomplexes of degree ≤d and shifted pure .d -1/-dimensional simplicial complexes.

KW - Componentwise linear ideals

KW - Face numbers

KW - Sequential Cohen-Macaulayness

KW - Simplicial complex

KW - Stanley-Reisner rings

UR - http://www.scopus.com/inward/record.url?scp=85035041682&partnerID=8YFLogxK

U2 - https://doi.org/10.4171/JEMS/755

DO - https://doi.org/10.4171/JEMS/755

M3 - مقالة

SN - 1435-9855

VL - 19

SP - 3851

EP - 3865

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 12

ER -

Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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