Work

Gröbner fans of Specht ideals

Year: 2025

Type: article

Abstract: In this paper, we give the Gröbner fan and the state polytope of a Specht ideal [Formula: see text] explicitly. In particular, we show that the state polytope of [Formula: see text] for a partition [Formula: see text] is always a generalized permutohedron, and it is a (usual) permutohedron if and only if [Formula: see text] for some [Formula: see text].

Source: Journal of Algebra and Its Applications

DOI: 10.1142/s0219498826501720

Authors: Hidefumi Ohsugi, Kohji Yanagawa

Institutions: Kwansei Gakuin University, Kansai University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Awards: Construction of a unified theory for toric rings of lattice polytopes arising from combinatorial objects, Development of new methods in the theory of convex polytopes by combining new concepts of discrete geometry and the theory of Groebner bases, The study on ring theoretic properties and Groebner basis of Specht ideals