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Open AccessArticle

Odd Cycles and Hilbert Functions of Their Toric Rings

1
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan
2
Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8914, Japan
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 22; https://doi.org/10.3390/math8010022
Received: 3 December 2019 / Revised: 17 December 2019 / Accepted: 18 December 2019 / Published: 20 December 2019
(This article belongs to the Special Issue Current Trends on Monomial and Binomial Ideals)
Studying Hilbert functions of concrete examples of normal toric rings, it is demonstrated that for each 1 s 5 , an O-sequence ( h 0 , h 1 , , h 2 s 1 ) Z 0 2 s satisfying the properties that (i) h 0 h 1 h s 1 , (ii) h 2 s 1 = h 0 , h 2 s 2 = h 1 and (iii) h 2 s 1 i = h i + ( 1 ) i , 2 i s 1 , can be the h-vector of a Cohen-Macaulay standard G-domain. View Full-Text
Keywords: O-sequence; h-vector; flawless; toric ring; stable set polytope O-sequence; h-vector; flawless; toric ring; stable set polytope
MDPI and ACS Style

Hibi, T.; Tsuchiya, A. Odd Cycles and Hilbert Functions of Their Toric Rings. Mathematics 2020, 8, 22.

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