3 papers
math.AC2025
Initial ideals of generic ideals and variations of Moreno-Socías conjecture
Koichiro Tani
It is known that the initial ideals of generic ideals are the same. Moreno-Socías conjectured that the initial ideal of generic ideals with respect to the degree reverse lexicograp…
math.AC2025
Khovanskii bases of subalgebras arising from finite distributive lattices
Akihiro Higashitani, Koji Matsushita, Koichiro Tani
The notion of Khovanskii bases was introduced by Kaveh and Manon. It is a generalization of the notion of SAGBI bases for a subalgebra of polynomials. The notion of SAGBI bases was…
math.AC2024
Non-finitely generated monoids corresponding to finitely generated homogeneous subalgebras
Akihiro Higashitani, Koichiro Tani
The goal of this paper is to study the possible monoids appearing as the associated monoids of the initial algebra of a finitely generated homogeneous -subalgebra of a polyn…