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Combinatorics, Complexity, and ChanceA Tribute to Dominic Welsh$
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Geoffrey Grimmett and Colin McDiarmid

Print publication date: 2007

Print ISBN-13: 9780198571278

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198571278.001.0001

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FOURIER ANALYSIS ON FINITE ABELIAN GROUPS: SOME GRAPHICAL APPLICATIONS

FOURIER ANALYSIS ON FINITE ABELIAN GROUPS: SOME GRAPHICAL APPLICATIONS

Chapter:
(p.103) 7 FOURIER ANALYSIS ON FINITE ABELIAN GROUPS: SOME GRAPHICAL APPLICATIONS
Source:
Combinatorics, Complexity, and Chance
Author(s):

Andrew Goodall

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198571278.003.0007

This article reviews basic techniques of Fourier analysis on a finite abelian group Q, with subsequent applications in graph theory. These include evaluations of the Tutte polynomial of a graph G in terms of cosets of the Q-flows of G. Other applications to spanning trees of Cayley graphs and to group-valued models on phylogenetic trees are also presented to illustrate methods.

Keywords:   Fourier analysis, abelian groups, graph theory, Tutte polynomial, Cayley graphs, phylogenetic trees

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