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.
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
SN - 0003-889X
VL - 88
SP - 507
EP - 512
JO - Archiv der Mathematik
JF - Archiv der Mathematik
IS - 6
ER -