17 citations · 55 across the 17 of their papers we have counts for
17 papers
An axiomatic framework from splitting and merging in MAT-labeled graphs, vines, and single-peaked domains
Hung Manh Tran, Tan Nhat Tran, Shuhei Tsujie
In recent work (Forum Math. Sigma, 2024), we established a correspondence between MAT-labeled graphs arising from hyperplane arrangements and regular vines from probability theory.…
Worpitzky-compatible sets and the freeness of arrangements between Shi and Catalan
Takuro Abe, Tan Nhat Tran
Given an irreducible root system, the Worpitzky-compatible subsets are defined by a geometric property of the alcoves inside the fundamental parallelepiped of the root system. This…
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…
Inductive and divisional posets
Roberto Pagaria, Maddalena Pismataro, Tan Nhat Tran +1
We call a poset factorable if its characteristic polynomial has all positive integer roots. Inspired by inductive and divisional freeness of a central hyperplane arrangement, we in…
A type analog of Ish arrangement
Tan Nhat Tran, Shuhei Tsujie
The Shi arrangement due to Shi (1986) and the Ish arrangement due to Armstrong (2013) are deformations of the type Coxeter arrangement that share many common properties. Motiva…
MAT-free graphic arrangements and a characterization of strongly chordal graphs by edge-labeling
Tan Nhat Tran, Shuhei Tsujie
Ideal subarrangements of a Weyl arrangement are proved to be free by the multiple addition theorem (MAT) due to Abe-Barakat-Cuntz-Hoge-Terao (2016). They form a significant class a…