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Lattice Paths Between Diagonal Boundaries
1998
Electronic Journal of Combinatorics
A bivariate symmetric backwards recursion is of the form $d[m,n]=w_{0}(d[m-1,n]+d[m,n-1])+\omega_{1}(d[m-r_{1},n-s_{1}]+d[m-s_{1},n-r_{1}])+\dots+\omega_{k}(d[m-r_{k},n-s_{k}]+d[m-s_{k},n-r_{k}])$ where $\omega_{0},\dots\omega_{k}$ are weights, $r_{1},\dots r_{k}$ and $s_{1},\dots s_{k}$ are positive integers. We prove three theorems about solving symmetric backwards recursions restricted to the diagonal band $x+u < y < x-l$. With a solution we mean a formula that expresses $d[m,n]$ as a sum of
doi:10.37236/1368
fatcat:wo3x6mvcy5fi3ktgmt3slokgs4