Counting pairs of nonintersecting lattice paths with respect to weighted turns Original Research Article

A formula involving a difference of the products of four q-binomial coefficients is shown to count pairs of nonintersecting lattice paths having a prescribed number of weighted turns. The weights are assigned to account for the location of the turns according to the major and lesser indices. The result, which is a q-analogue of a variant of the formula of Kreweras and Poupard, is proved bijectively; however, when q ≠ 1 the bijection is defined inductively.