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.
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In Memory of Gian-Carlo Rota
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Bonin, J.E. Strongly inequivalent representations and Tutte polynomials of matroids. Algebra univers. 49, 289–303 (2003). https://doi.org/10.1007/s00012-003-1718-3
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DOI: https://doi.org/10.1007/s00012-003-1718-3