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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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EXPANDING THE TUTTE POLYNOMIAL OF A MATROID OVER THE INDEPENDENT SETS

EXPANDING THE TUTTE POLYNOMIAL OF A MATROID OVER THE INDEPENDENT SETS

Chapter:
(p.172) 11 EXPANDING THE TUTTE POLYNOMIAL OF A MATROID OVER THE INDEPENDENT SETS
Source:
Combinatorics, Complexity, and Chance
Author(s):

Koko Kalambay Kayibi

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198571278.003.0011

This chapter provides direct combinatorial proof of an expansion of the Tutte polynomial by independent sets of the matroid. Another expansion of the Tutte polynomial is presented in terms of spanning sets. In the process, it is shown that there is a partition of the set of independent sets of a matroid, such that if the independent set I and the basis B are contained in the same part of the partition, the external activity of I is equal to the external activity of B.

Keywords:   Tutte polynomial, matroids, spanning sets, partition

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