Counterexamples to a conjecture of Las Vergnas

2018/09/04 by Brijder, Robert, Hoogeboom, Hendrik Jan
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.00813

Abstract

We present counterexamples to a 30-year-old conjecture of Las Vergnas [J. Combin. Theory Ser. B, 1988] regarding the Tutte polynomial of binary matroids.

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• The Las Vergnas Polynomial for embedded graphs
• K-theoretic Tutte polynomials of morphisms of matroids
• The Tutte polynomials of genus g
• The Merino--Welsh conjecture is false for matroids
• The Tutte q-Polynomial