8 papers
The Coboundary Quasi-Polynomials of Hyperplane Arrangements over Residually Finite Dedekind Domains
Masamichi Kuroda, Norihiro Nakashima, Shuhei Tsujie
The characteristic polynomial plays an important role in study of hyperplane arrangements. There are several refinements of the characteristic polynomial. One of them is the coboun…
On gapped repeats in a cyclic Fibonacci word
Takashi Horiyama, Yasuhide Numata, Kazuhisa Seto +1
In this article, we consider the words with cyclic indices. For given , we consider the pair of indices such that the word of length from is equal to the word…
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.…
Convolution, cumulants and infinitesimal generators in the formal power series ring
Shuhei Tsujie, Yuki Ueda
We extend the notions of finite free convolution and finite free cumulants to the setting of formal power series by introducing their natural analogues, namely -deformed convolu…
Exponents of 2-multiarrangements of three lines over fields of positive characteristic
Shuhei Tsujie, Ryo Uchiumi
Wakamiko determined bases and the exponents for multiarrangements of three lines over a field of characteristic zero. In this paper, we study the exponents of multiarrangements of…
Signatures of Type Root Systems
Michael Cuntz, Hung Manh Tran, Tan Nhat Tran +1
Given a type root system of rank , we introduce the concept of a signature for each subset of consisting of positive roots. For a subset represented…