3 papers
math.AG2025
Uniform bases for ideal arrangements
Makoto Enokizono, Tatsuya Horiguchi, Takahiro Nagaoka +1
In this paper we introduce and study uniform bases for the ideal arrangements in all Lie types. Explicit uniform bases are given by Abe-Horiguchi-Masuda-Murai-Sato for types $A,B,C…
math.CO2025
Gamma vectors of partitioned permutohedra
Tatsuya Horiguchi, Mikiya Masuda, Takashi Sato +2
We determine that -vectors of partitioned permutohedra, thereby generalizing a result of Foata and Schützenberger. Our result is closely related to a result of Athanasiadis on…
math.AG2024
Coordinate rings of regular nilpotent Hessenberg varieties in the open opposite Schubert cell
Tatsuya Horiguchi, Tomoaki Shirato
Dale Peterson has discovered a surprising result that the quantum cohomology ring of the flag variety $\mbox{GL}_n(\mathbb{C})/B$ is isomorphic to the coordinate ring of the inters…