17 citations · 85 across the 28 of their papers we have counts for
29 papers
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 of…
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…
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…
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 by…
-deformation of chromatic polynomials and graphical arrangements
Tongyu Nian, Shuhei Tsujie, Ryo Uchiumi +1
We first observe a mysterious similarity between the braid arrangement and the arrangement of all hyperplanes in a vector space over the finite field . These two arra…
Freeness of hyperplane arrangements associated with gain graphs
Daisuke Suyama, Michele Torielli, Shuhei Tsujie
Athanasiadis studied arrangements obtained by adding shifted hyperplanes to the braid arrangement. Similarly, Bailey studied arrangements obtained by adding tilted hyperplanes to t…
Universal graph series, chromatic functions, and their index theory
Tsuyoshi Miezaki, Akihiro Munemasa, Yusaku Nishimura +2
In the present paper, we introduce the concept of universal graph series. We then present four invariants of graphs and discuss some of their properties. In particular, one of thes…
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…
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…
Upper Embeddability of Graphs and Products of Transpositions Associated with Edges
Shuhei Tsujie, Ryo Uchiumi
Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing a linear order on the edge set, we obtain a permutation of the vertices. Dénes…
The Characteristic Quasi-Polynomials of Hyperplane Arrangements over Residually Finite Dedekind Domains
Masamichi Kuroda, Shuhei Tsujie
Kamiya, Takemura, and Terao initiated the theory of the characteristic quasi-polynomial of an integral arrangement, which is a function counting the elements in the complement of t…
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…
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…
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…
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…
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…
Enumeration of Flats of the Extended Catalan and Shi Arrangements with Species
Norihiro Nakashima, Shuhei Tsujie
The number of flats of a hyperplane arrangement is considered as a generalization of the Bell number and the Stirling number of the second kind. Robert Gill gave the exponential ge…
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…
Freeness of Hyperplane Arrangements between Boolean Arrangements and Weyl Arrangements of Type
Michele Torielli, Shuhei Tsujie
Every subarrangement of Weyl arrangements of type is represented by a signed graph. Edelman and Reiner characterized freeness of subarrangements between type $ A_{\ell…
The Chromatic Symmetric Functions of Trivially Perfect Graphs and Cographs
Shuhei Tsujie
Richard P. Stanley defined the chromatic symmetric function of a simple graph and has conjectured that every tree is determined by its chromatic symmetric function. Recently, Takah…
Signed graphs and the freeness of the Weyl subarrangements of type
Daisuke Suyama, Michele Torielli, Shuhei Tsujie
A Weyl arrangement is the hyperplane arrangement defined by a root system. Arnold and Saito proved that every Weyl arrangement is free. The Weyl subarrangements of type …
A Generalization of APN Functions for Odd Characteristic
Masamichi Kuroda, Shuhei Tsujie
Almost perfect nonlinear (APN) functions on finite fields of characteristic two have been studied by many researchers. Such functions have useful properties and applications in cry…