Chapter

FOURIER ANALYSIS ON FINITE ABELIAN GROUPS: SOME GRAPHICAL APPLICATIONS

Andrew Goodall

in Combinatorics, Complexity, and Chance

Published in print January 2007 | ISBN: 9780198571278
Published online September 2007 | e-ISBN: 9780191718885 | DOI: https://dx.doi.org/10.1093/acprof:oso/9780198571278.003.0007

Series: Oxford Lecture Series in Mathematics and Its Applications

 FOURIER ANALYSIS ON FINITE ABELIAN GROUPS: SOME GRAPHICAL APPLICATIONS

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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

Chapter.  14520 words. 

Subjects: Probability and Statistics

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