arXiv subjects
Publications and source records attributed to Yohei Oshida.
In this paper, we introduce a method for reducing the calculation time of matrix exponentiation calculations on numerical max-plus algebra. In particular, we explain Ghost-OSD Method that can quickly calculate the powers of honest matrix. For more information on this abstract, see the PDF.
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. It was introduced by Yohei Oshida in 2022. The Crystal module in the title is the residue class ring which is in relation to the join-meet ideal of Crystal lattice. In this paper, we give important inequalities about the minimal free resolution of the Crystal module. The important point about this result is that the projective dimension and Betti-number of the Crystal module can be evaluated by using the Koszul complex.
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.
In this paper, we give new examples of a finite lattice $L$ such that the join-meet ideal $I_L$ is radical.