TY - JOUR

T1 - Maximal Betti numbers of Cohen-Macaulay complexes with a given f-vector

AU - Murai, Satoshi

AU - Hibi, Takayuki

N1 - Funding Information:
The first author is supported by JSPS Research Fellowships for Young Scientists.
Copyright:
Copyright 2007 Elsevier B.V., All rights reserved.

PY - 2007/6

Y1 - 2007/6

N2 - Given the f-vector f = (f 0, f 1, . . .) of a Cohen-Macaulay simplicial complex, it will be proved that there exists a shellable simplicial complex Δ f with f(Δ f ) = f such that, for any Cohen-Macaulay simplicial complex Δ with f(Δ) = f, one has βi(Δ ≤ βi I Δ_ for all i and j, where f(Δ) is the f-vector of Δ and where β ij (I Δ) are graded Betti numbers of the Stanley-Reisner ideal I Δ of Δ.

AB - Given the f-vector f = (f 0, f 1, . . .) of a Cohen-Macaulay simplicial complex, it will be proved that there exists a shellable simplicial complex Δ f with f(Δ f ) = f such that, for any Cohen-Macaulay simplicial complex Δ with f(Δ) = f, one has βi(Δ ≤ βi I Δ_ for all i and j, where f(Δ) is the f-vector of Δ and where β ij (I Δ) are graded Betti numbers of the Stanley-Reisner ideal I Δ of Δ.

KW - Cohen-Macaulay simplicial complex

KW - F-vector

KW - Graded Betti number

KW - H-vector

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U2 - 10.1007/s00013-007-1880-5

DO - 10.1007/s00013-007-1880-5

M3 - Article

AN - SCOPUS:34347264154

VL - 88

SP - 507

EP - 512

JO - Archiv der Mathematik

JF - Archiv der Mathematik

SN - 0003-889X

IS - 6

ER -