A Tutte polynomial inequality for lattice path matroids

Kolja Knauer, Leonardo Martínez-Sandoval, Jorge Luis Ramírez Alfonsín

Let $M$ be a matroid without loops or coloops and let $T(M;x,y)$ be its Tutte polynomial. In 1999 Merino and Welsh conjectured that $$\max (T(M;2,0),T(M;0,2))\ge T(M;1,1)$$ holds…