Betti numbers of lex ideals over some Macaulay-Lex rings |
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Authors: | Jeff Mermin Satoshi Murai |
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Institution: | 1.Department of Mathematics,University of Kansas,Lawrence,USA;2.Department of Mathematics, Graduate School of Science,Kyoto University,Kyoto,Japan |
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Abstract: | Let A=Kx
1,…,x
n
] be a polynomial ring over a field K and M a monomial ideal of A. The quotient ring R=A/M is said to be Macaulay-Lex if every Hilbert function of a homogeneous ideal of R is attained by a lex ideal. In this paper, we introduce some new Macaulay-Lex rings and study the Betti numbers of lex ideals
of those rings. In particular, we prove a refinement of the Frankl–Füredi–Kalai Theorem which characterizes the face vectors
of colored complexes. Additionally, we disprove a conjecture of Mermin and Peeva that lex-plus-M ideals have maximal Betti numbers when A/M is Macaulay-Lex. |
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Keywords: | |
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