Odd Cycles and Hilbert Functions of Their Toric Rings

Takayuki Hibi and Akiyoshi Tsuchiya
Additional contact information
Takayuki Hibi: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan
Akiyoshi Tsuchiya: Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8914, Japan

Mathematics, 2019, vol. 8, issue 1, 1-4

Abstract: 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.

Keywords: O -sequence; h -vector; flawless; toric ring; stable set polytope (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/1/22/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/1/22/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2019:i:1:p:22-:d:300424

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().