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math.CO2021
Freeness for restriction arrangements of the extended Shi and Catalan arrangements
Norihiro Nakashima, Shuhei Tsujie
The extended Shi and Catalan arrangements are well investigated arrangements. In this paper, we prove that the cone of the extended Catalan arrangement of type A is always heredita…
math.CO2021
Vertex-weighted Digraphs and Freeness of Arrangements Between Shi and Ish
Takuro Abe, Tan Nhat Tran, Shuhei Tsujie
We introduce and study a digraph analogue of Stanley's -graphical arrangements from the perspectives of combinatorics and freeness. Our arrangements form a common generalization…
math.CO2021
Chromatic Signed-Symmetric Functions of Signed Graphs
Masamichi Kuroda, Shuhei Tsujie
Stanley introduced the chromatic symmetric function of a simple graph, which is a generalization of a chromatic polynomial. This is expressed in terms of the integer points of the…