Counting filter restricted paths in Z^2 lattice
Ol'ga Viktorovna Postnova, Dmitry Solovyev · Enumerative Combinatorics and Applications · 2024
We derive a path counting formula for two-dimensional lattice path model on a plane with filter restrictions.A filter is a line that restricts the path passing it to one of possible directions.Moreover, each path that touches this line is assigned a special weight.The periodic filter restrictions are motivated by the problem of tensor power decomposition for representations of quantum sl 2 at roots of unity.Our main result is the explicit formula for the weighted number of paths from the origin to a fixed point between two filters in this model.