The Coefficients of the Tutte Polynomial Are Not Unimodal

W. T. Tutte conjectured that the coefficients ti, j of his dichromate form unimodal sequences in i and j separately. P. D. Seymour and D. J. A. Welsh conjectured more generally that the same holds for the coefficients of the Tutte polynomial of an arbitrary matroid. We show, by an example, that these conjectures do not hold.