3 problems

Let $\mathcal{M}$ be the class of lattice path matroids. The class is efficiently pigeonhole when the relevant pigeonhole bounds can be obtained efficiently. Efficient pigeonhole c…

Let $M$ be a matroid without loops or coloops, and let $T(M;x,y)$ be its Tutte polynomial. Matroidal Merino–Welsh conjectures. The following inequalities hold: … … and … These conj…

Let $\Gamma$ be a lattice path polymatroid. Its base ring is the polynomial ring $\mathbb{C}[Y_m: m$ is a basis of $\Gamma]$, and its toric ideal is the kernel of the map … defined…