On cographic regular matroids |
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Authors: | James G. Oxley |
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Affiliation: | Mathematical Institute, 24–29 St. Giles, Oxford OX1 3LB, England |
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Abstract: | The presentation of alternating permutatioas via labelled binary trees is used to define polynomials H2n?1(x) as enumerating polynomials for the height of peaks in alternating permutations of length 2n?1. A divisibility property of the coefficients of these polynomials is proved, which generalizes and explains combinatirially a well-known property of the tangent numbers. Furthermore, a version of the exponential generating function for the H2n?1(x) is given, leading to a new combinatorial interpretation of Dumont's modified Ghandi-polynomials. |
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