6 papers
Cartwright--Sturmfelsness of complementary determinantal edge ideals
Koichiro Tani
We introduce complementary determinantal edge ideals. For a graph on vertices, the complementary determinantal edge ideal is generated by the maximal minors of a…
Algebras with straightening laws on join- or meet-semidistributive lattices
Koji Matsushita, Sora Miyashita, Koichiro Tani
We study algebras with straightening laws on join- or meet-semidistributive lattices. We show that for a join-semidistributive (resp. meet-semidistributive) lattice, meet-distribut…
Standard multigraded Hibi rings and Cartwright-Sturmfels ideals
Koji Matsushita, Koichiro Tani
In this paper, we introduce standard multigradings on Hibi rings, which are algebras arising from posets. We show that any standard multigrading on a Hibi ring that makes its defin…
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…
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…
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…