A Remarkable Formula for Counting Nonintersecting Lattice Paths in a Ladder with Respect to Turns
نویسنده
چکیده
We prove a formula, conjectured by Conca and Herzog, for the number of all families of nonintersecting lattice paths with certain starting and end points in a region that is bounded by an upper ladder. Thus we are able to compute explicitly the Hilbert series for certain one-sided ladder determinantal rings.
منابع مشابه
A determinantal formula for the Hilbert series of one-sided ladder determinantal rings
We give a formula that expresses the Hilbert series of one-sided ladder determinantal rings, up to a trivial factor, in form of a determinant. This allows the convenient computation of these Hilbert series. The formula follows from a determinantal formula for a generating function for families of nonintersecting lattice paths that stay inside a one-sided ladder-shaped region, in which the paths...
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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 bijectivel...
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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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تاریخ انتشار 1998