Strongly inequivalent representations and Tutte polynomials of matroids |
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Authors: | Email author" target="_blank">Joseph?E?BoninEmail author |
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Institution: | (1) Department of Mathematics, The George Washington University, ., 20052 Washington, D.C., USA |
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Abstract: | We develop constructive techniques to show that non-isomorphic 3-connected
matroids that are representable over a fixed finite field and that have the same Tutte
polynomial abound. In particular, for most prime powers q,
we construct infinite families
of sets of 3-connected matroids for which the matroids in a given set are non-isomorphic,
are representable over GF(q), and have the same Tutte
polynomial. Furthermore, the
cardinalities of the sets of matroids in a given family grow exponentially as a function of
rank, and there are many such families.In Memory of Gian-Carlo Rota |
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Keywords: | 05B35 06C10 51E20 |
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