2022/03/14 by Yohei Oshida, Oshida, Yohei
Computer Science · Mathematics · #06A11 #06B05 #13A02 #13P10 #Advanced Combinatorial Mathematics #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2203.06939
openalex publication_date 2022/03/14 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
The join-meet ideal was introduced by Takayuki Hibi in 1987. It is binomial ideals that are defined by finite lattices. We study the join-meet ideal of non-distributive finite lattices that do not always satisfy modular. In particular, we work on the case of Crystal lattice which is one of them. In this paper, we give the computational result of a total of each of the 1-th and 2-th of grade Betti numbers of the join-meet ideal of a special Crystal lattice. The important point about this result is that it is characterized by the number of combinations of special generators. Moreover, we can consider from this result that a compatible monomial order suggests a connection to something good.