Lattice Polynomials, 12312-Avoiding Partial Matchings and Even Trees

William Y. C. Chen, Louis W. Shapiro, Susan Y. J. Wu

The lattice polynomials $L_{i,j}(x)$ are introduced by Hough and Shapiro as a weighted count of certain lattice paths from the origin to the point $(i,j)$. In particular, $L_{2n, n…