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Odd Cycles and Hilbert Functions of Their Toric Rings

Author

Listed:
  • 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)

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.

Suggested Citation

  • Takayuki Hibi & Akiyoshi Tsuchiya, 2019. "Odd Cycles and Hilbert Functions of Their Toric Rings," Mathematics, MDPI, vol. 8(1), pages 1-4, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2019:i:1:p:22-:d:300424
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