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A collection of sets related to the tutte polynomial of a matroid

Part of the Lecture Notes in Mathematics book series (LNM,volume 1073)

Abstract

It is known that if we order the edges of a graph, or more generally, elements of a matroid, then each spanning forest, or basis, B has a subset ψ(B) of "internally passive" elements, and for each forest, or independent set, F, there is a unique basis B such that ψ(B) ⊆ F ⊆ B. In the context of matroids generally, we examine the structure of the collection of sets {ψ(B) : B is a basis}, particularly looking at the sequence of numbers of these sets of each cardinality, which we conjecture is log-concave.

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References

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© 1984 Springer-Verlag

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Dawson, J.E. (1984). A collection of sets related to the tutte polynomial of a matroid. In: Koh, K.M., Yap, H.P. (eds) Graph Theory Singapore 1983. Lecture Notes in Mathematics, vol 1073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073117

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  • DOI: https://doi.org/10.1007/BFb0073117

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13368-1

  • Online ISBN: 978-3-540-38924-8

  • eBook Packages: Springer Book Archive