S. Murai

activity

20052026

most citedBetti numbers of symmetric shifted ideals

19 citations · 137 across the 55 of their papers we have counts for

collaborators

58 papers

math.AC2026

A criterion for determinantal presentations of numerical semigroup rings

Satoshi Murai, Kou Takahashi

We study numerical semigroups whose defining ideals admit determinantal presentations by the $2 \times 2$ minors of a $2 \times n$ matrix. A conjecture of Cuong, Kien, Matsuoka, and T…

math.CO2023

Ehrhart quasi-polynomials and parallel translations

Akihiro Higashitani, Satoshi Murai, Masahiko Yoshinaga

Given a rational polytope $P \subset R^{d}$ , the numerical function counting lattice points in the integral dilations of $P$ is known to become a quasi-polynomial, called the…

math.CO2023

Affine stresses, inverse systems, and reconstruction problems

Satoshi Murai, Isabella Novik, Hailun Zheng

A conjecture of Kalai asserts that for $d \geq 4$ , the affine type of a prime simplicial $d$ -polytope $P$ can be reconstructed from the space of affine $2$ -stresses of $P$ . We prove…

math.AC2021

A note on the reducedness and Gröbner bases of Specht ideals

Satoshi Murai, Hidefumi Ohsugi, Kohji Yanagawa

The Specht ideal of shape $λ$ , where $λ$ is a partition, is the ideal generated by all Specht polynomials of shape $λ$ . Haiman and Woo proved that these ideals are reduced and foun…

math.AC2020★ 9 cited

An equivariant Hochster's formula for $S_{n}$ -invariant monomial ideals

Satoshi Murai, Claudiu Raicu

Let $R = k [x_{1}, \dots, x_{n}]$ be a polynomial ring over a field $k$ and let $I \subset R$ be a monomial ideal preserved by the natural action of the symmetric group $\mathfrak S_…

math.CO2020★ 3 cited

Strictness of the log-concavity of generating polynomials of matroids

Satoshi Murai, Takahiro Nagaoka, Akiko Yazawa

Recently, it was proved by Anari-Oveis Gharan-Vinzant, Anari-Liu-Oveis Gharan-Vinzant and Brändén-Huh that, for any matroid $M$ , its basis generating polynomial and its independent…