2019/12/16 by Takayuki Hibi, Akiyoshi Tsuchiya
Computer Science · Mathematics · #Commutative Algebra and Its Applications #Generalization #Hilbert R-tree #Hilbert scheme #Hilbert series and Hilbert polynomial #Hilbert space #Hilbert–Poincaré series #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC #math.CO #msc:13A02 #msc:13H10
paper · pdf · doi:10.3390/math8010022
published as Mathematics 8 (2020), 22 · 4 pages
openalex created_date 2019/12/13 · arxiv created 2019/12/16 · openalex publication_date 2019/12/20 · arxiv updated 2020/09/07 · openalex updated_date 2026/08/06
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.