1 citations · 1 across the 3 of their papers we have counts for
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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…
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…
Period collapse in characteristic quasi-polynomials of hyperplane arrangements
Akihiro Higashitani, Tan Nhat Tran, Masahiko Yoshinaga
Given an integral hyperplane arrangement, Kamiya-Takemura-Terao (2008 & 2011) introduced the notion of characteristic quasi-polynomial, which enumerates the cardinality of the comp…
Expectations of Tutte-related functions of random ranked sets with multiplicities
Tan Nhat Tran
Employing two models, we show that various counting functions of a random variable defined by restriction or contraction of a ranked set with multiplicity (e.g., classical and arit…