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New co-authored scientific article by our resercher Gergely Kál Csáji is published in Advances in Mathematics journal


The Merino–Welsh conjecture is false for matroids


Advances in Mathematics




Advances in Mathematics – Volume 446, June 2024 – Available online 25 April 2024


Abstract: The matroidal version of the Merino–Welsh conjecture states that the Tutte polynomial TM(x,y) of any matroid M without loops and coloops satisfies that

Equivalently, if the Merino–Welsh conjecture is true for all matroids without loops and coloops, then the following inequalities are also satisfied for all matroids without loops and coloops: TM(2,0)+TM(0,2)⩾2TM(1,1), andTM(2,0)TM(0,2)⩾TM(1,1)2. We show a counter-example for these inequalities.

MSC: primary 05C30, secondary 05C31, 05C70


Keywords: Tutte polynomial, Merino–Welsh conjecture