Zobrazeno 1 - 10
of 163
pro vyhledávání: '"Tsuchiya, Akiyoshi"'
Autor:
Matsushita, Koji, Tsuchiya, Akiyoshi
The codegree ${\rm codeg}(P)$ of a lattice polytope $P$ is a fundamental invariant in discrete geometry. In the present paper, we investigate the codegree of the stable set polytope $P_G$ associated with a graph $G$. Specifically, we establish the in
Externí odkaz:
http://arxiv.org/abs/2412.10090
Autor:
Tran, Tan Nhat, Tsuchiya, Akiyoshi
Publikováno v:
Comptes Rendus. Mathématique, Vol 359, Iss 6, Pp 665-674 (2021)
The class of Worpitzky-compatible subarrangements of a Weyl arrangement together with an associated Eulerian polynomial was recently introduced by Ashraf, Yoshinaga and the first author, which brings the characteristic and Ehrhart quasi-polynomials i
Externí odkaz:
https://doaj.org/article/3b164ca1882249cd931d4cd21be61b09
Autor:
Ohsugi, Hidefumi, Tsuchiya, Akiyoshi
Kempe equivalence is a classical and important notion on vertex coloring in graph theory. In the present paper, we introduce several ideals associated with graphs and provide a method to determine whether two $k$-colorings are Kempe equivalent via co
Externí odkaz:
http://arxiv.org/abs/2401.06027
Autor:
Ohsugi, Hidefumi, Tsuchiya, Akiyoshi
Perfectly contractile graphs form a typical class of perfect graphs. In particular, all $k$-colorings of a perfectly contractile graph are Kempe equivalent. Everett and Reed conjectured that a graph is perfectly contractile if and only if it contains
Externí odkaz:
http://arxiv.org/abs/2303.12824
Autor:
Ohsugi, Hidefumi, Tsuchiya, Akiyoshi
Publikováno v:
Discrete and Computational Geometry 70 (2023), 214--235
PQ-type adjacency polytopes $\nabla^{\rm PQ}_G$ are lattice polytopes arising from finite graphs $G$. There is a connection between $\nabla^{\rm PQ}_G$ and the engineering problem known as power-flow study, which models the balance of electric power
Externí odkaz:
http://arxiv.org/abs/2103.15045
Publikováno v:
Collectanea Mathematica 74 (2023), 333--351
A directed edge polytope $\mathcal{A}_G$ is a lattice polytope arising from root system $A_n$ and a finite directed graph $G$. If every directed edge of $G$ belongs to a directed cycle in $G$, then $\mathcal{A}_G$ is terminal and reflexive, that is,
Externí odkaz:
http://arxiv.org/abs/2103.06404
Autor:
Tsuchiya, Akiyoshi
It is known that the sectional genus of a polarized variety has an upper bound, which is an extension of the Castelnuovo bound on the genus of a projective curve. Polarized varieties whose sectional genus achieves this bound are called Castelnuovo. O
Externí odkaz:
http://arxiv.org/abs/2010.13617
Publikováno v:
Journal of Algebra 593 (2022), 550--567
In the present paper, we give a complete classification of connected simple graphs whose edge rings have a $q$-linear resolution with $q \geq 2$. In particular, we show that the edge ring of a finite connected simple graph with a $q$-linear resolutio
Externí odkaz:
http://arxiv.org/abs/2010.02854
Autor:
Ohsugi, Hidefumi, Tsuchiya, Akiyoshi
Publikováno v:
Combinatorial Theory 1 (2021), #9
Symmetric edge polytopes $\mathcal{A}_G$ of type A are lattice polytopes arising from the root system $A_n$ and finite simple graphs $G$. There is a connection between $\mathcal{A}_G$ and the Kuramoto synchronization model in physics. In particular,
Externí odkaz:
http://arxiv.org/abs/2008.08621
Autor:
Tran, Tan Nhat, Tsuchiya, Akiyoshi
Publikováno v:
Comptes Rendus. Math\'ematique 359 (2021), 665--674
The class of Worpitzky-compatible subarrangements of a Weyl arrangement together with an associated Eulerian polynomial was recently introduced by Ashraf, Yoshinaga and the first author, which brings the characteristic and Ehrhart quasi-polynomials i
Externí odkaz:
http://arxiv.org/abs/2007.01248