Vertex-Face/Zeta correspondence

We present the characteristic polynomial for the transition matrix of a vertex-face walk on a graph, and obtain its spectra. Furthermore, we express the characteristic polynomial for the transition matrix of a vertex-face walk on the 2-dimensional torus by using its adjacency matrix, and obtain its...

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Veröffentlicht in:	Journal of algebraic combinatorics 2022-09, Vol.56 (2), p.527-545
Hauptverfasser:	Komatsu, Takashi, Konno, Norio, Sato, Iwao
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Computer Science Convex and Discrete Geometry Group Theory and Generalizations Lattices Mathematics Mathematics and Statistics Order Ordered Algebraic Structures Polynomials Spectra Toruses
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container_title	Journal of algebraic combinatorics
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creator	Komatsu, Takashi Konno, Norio Sato, Iwao
description	We present the characteristic polynomial for the transition matrix of a vertex-face walk on a graph, and obtain its spectra. Furthermore, we express the characteristic polynomial for the transition matrix of a vertex-face walk on the 2-dimensional torus by using its adjacency matrix, and obtain its spectra. As an application, we define a new walk-type zeta function with respect to the transition matrix of a vertex-face walk on the two-dimensional torus, and present its explicit formula.
doi_str_mv	10.1007/s10801-022-01122-5
format	Article
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subjects	Combinatorics Computer Science Convex and Discrete Geometry Group Theory and Generalizations Lattices Mathematics Mathematics and Statistics Order Ordered Algebraic Structures Polynomials Spectra Toruses
title	Vertex-Face/Zeta correspondence
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