Counting pairs of nonintersecting lattice paths with respect to weighted turns
نویسندگان
چکیده
A formula involving a diierence of the products of four q-binomial coeecients 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 6 = 1 the bijection is deened inductively.
منابع مشابه
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A theory of counting nonintersecting lattice paths by the major index and generalizations of it is developed. We obtain determinantal expressions for the corresponding generating functions for families of nonintersecting lattice paths with given starting points and given nal points, where the starting points lie on a line parallel to x + y = 0. In some cases these determinants can be evaluated ...
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A theory of counting nonintersecting lattice paths by the major index and generalizations of it is developed. We obtain determinantal expressions for the corresponding generating functions for families of nonintersecting lattice paths with given starting points and given final points, where the starting points lie on a line parallel to x+y = 0. In some cases these determinants can be evaluated ...
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 153 شماره
صفحات -
تاریخ انتشار 1996