2013/09/12 by Thanh Vu, Vu, Thanh
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.CO
paper · pdf · doi:10.48550/arxiv.1309.3033
12 pages
arxiv created 2013/09/12 · openalex publication_date 2013/09/12 · arxiv updated 2013/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K be an arbitrary field. Let n,d ≥ 2 be positive integers. Let V(n,d) be the set of all lattice points \mathbf b = (b1, ..., bn) in \mathbb Nn such that ∑i=1n bi = d. Let Γ= V(n,d) ∖ \ \mathbf a \ for some element \mathbf a ∈ V(n,d). In this paper we prove that the semigroup ring K[Γ] is Koszul unless d ≥ 3 and \mathbf a = (0, ...,0, 2, d-2) or one of its permutations. This generalizes results of Caviglia, Conca, and Tancer.