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5 papers · 1 filter
Vines and MAT-labeled graphs
Hung Manh Tran, Tan Nhat Tran, Shuhei Tsujie
The present paper explores a connection between two concepts arising from different fields of mathematics. The first concept, called vine, is a graphical model for dependent random…
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…
Modular Construction of Free Hyperplane Arrangements
Shuhei Tsujie
In this article, we study freeness of hyperplane arrangements. One of the most investigated arrangement is a graphic arrangement. Stanley proved that a graphic arrangement is free…
Unit Ball Graphs on Geodesic Spaces
Masamichi Kuroda, Shuhei Tsujie
Consider finitely many points in a geodesic space. If the distance of two points is less than a fixed threshold, then we regard these two points as "near". Connecting near points w…
A basis construction of the extended Catalan and Shi arrangements of the type
Takuro Abe, Daisuke Suyama
In [9], Terao proved the freeness of multi-Coxeter arrangements with constant multiplicities by giving an explicit construction of bases. Combining it with algebro-geometric method…