A direct inductive proof of the sharp Merino--Welsh threshold for matroids

Jungang Chen, Jiaxin Xie

Motivated by the Merino--Welsh conjecture, we consider the smallest $c\ge 0$, denoted by $c_{\ast }$, for which the inequality $T_M(c,0)T_M(0,c)\ge T_M(1,1{)}^2$ holds for every loopless an…