arXiv subjects

Jongmin Lim

Publications and source records attributed to Jongmin Lim.

2 recordsLinked to original sources

arXiv2023

Lattice of Integer Flows and the Poset of Strongly Connected Orientations for Regular Matroids

A 2010 result of Amini provides a way to extract information about the structure of the graph from the geometry of the Voronoi polytope of the lattice of integer flows (which determines the graph up to two-isomorphism). Specifically, Amini shows that the face poset of the Voronoi polytope is isomorphic to the poset of strongly connected orientations of subgraphs. This answers a question raised by Caporaso and Viviani, and Amini also proves a dual result for integer cuts. In this paper we generalise Amini's result to regular matroids; in this context the theorem for integer cuts becomes a direct consequence of the theorem for integer flows, by making duality explicit as matroid duality.

math.CO↗

arXiv2023

On Schützenberger modules of the cactus group

The cactus group acts on the set of standard Young tableau of a given shape by (partial) Schützenberger involutions. It is natural to extend this action to the corresponding Specht module by identifying standard Young tableau with the Kazhdan-Lusztig basis. We term these representations of the cactus group "Schützenberger modules", denoted $S^λ_{\mathsf{Sch}}$, and in this paper we investigate their decomposition into irreducible components. We prove that when $λ$ is a hook shape, the cactus group action on $S^λ_{\mathsf{Sch}}$ factors through $S_{n-1}$ and the resulting multiplicities are given by Kostka coefficients. Our proof relies on results of Berenstein and Kirillov and Chmutov, Glick, and Pylyavskyy.

math.CO↗