Counting Nonintersecting Lattice Paths with Turns
نویسندگان
چکیده
We derive enumeration formulas for families of nonintersecting lattice paths with given starting and end points and a given total number of North-East turns. These formulas are important for the computation of Hilbert series for determinantal and pfaffian rings.
منابع مشابه
A Remarkable Formula for Counting Nonintersecting Lattice Paths in a Ladder with Respect to Turns
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.
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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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