Spanning tree invariants, loop systems and doubly stochastic matrices
type: Item
instance of: scholarly article
title: Spanning tree invariants, loop systems and doubly stochastic matrices
zbMATH Open document ID: 1187.15033
author: Ricardo Gómez
author: José Miguel Salazar
published in: Linear Algebra and its Applications
publication date: 2009-12-18T00:00:00Z
review text: \textit{D. Lind} and \textit{S. Tuncel} [Codes, systems, and graphical models. IMA workshop, Minneapolis, MN, USA, August 2--13, 1999. New York, NY: Springer. IMA Vol. Math. Appl. 123, 487--497 (2001; Zbl 1030.37005)] introduced an invariant of block isomorphism for Markov shifts. The invariant is called a spanning tree invariant and is obtained by taking the weight of all spanning trees of a presentation of the Markov shift. This invariant is observed in the context of loop systems of Markov chains. For \(n=1,2,3\) the spanning tree invariants of the loop systems of a Markov chain determined by an irreducible stochastic matrix \(P\) of degree \(n\) coincide if and only if \(P\) is doubly stochastic; and in this case, the common value of the spanning tree invariants of the loop systems is \(n\).
reviewed by: Huang Wenxue
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 37A35
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 5649995
zbMATH Keywords: block isomorphism
zbMATH Keywords: doubly stochastic matrices
zbMATH Keywords: invariant
zbMATH Keywords: loop systems
zbMATH Keywords: Markov chain
zbMATH Keywords: Markov shift
zbMATH Keywords: spanning tree
zbMATH Keywords: stochastic zeta function
zbMATH Keywords: weight
zbMATH Keywords: irreducible stochastic matrix
MaRDI profile type: Publication
full work available at URL: j.laa.2009.09.002
OpenAlex ID: W2136148437
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DOI: 10.1016/J.LAA.2009.09.002
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description: scientific article; zbMATH DE number 5649995