Moments of Directed Paths in a Wedge
نویسندگان
چکیده
منابع مشابه
Partially directed paths in a symmetric wedge
The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and its solution. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to a symmetric wedge...
متن کاملPartially directed paths in a wedge
The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and solving for it. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to both a symmetri...
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We give a bijection between partially directed paths in the symmetric wedge y = ±x and matchings, which sends north steps to nestings. This gives a bijective proof of a result of Prellberg et al. that was first discovered through the corresponding generating functions: the number of partially directed paths starting at the origin confined to the symmetric wedge y = ±x with k north steps is equa...
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Abstract: Consider lattice paths in the plane allowing the steps (1,1), (1,-1), and (w,0), for some nonnegative integer w. For n > 1, let E(n,0) denote the set of paths from (0,0) to (n,0) running strictly above the x-axis except initially and finally. Generating functions are given for sums of moments of the ordinates of the lattice points on the paths in E(n,0). In particular, recurrencess ar...
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Kasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain q-analogues of Laguerre and Charlier polynomials. The moments of these orthogonal polynomials have combinatorial models in terms of crossings in permutations and set partitions. The aim of this article is to prove simple formulas for the moments of the q-Laguerre and the q-Charlier polynomials, in the style of the Touchard...
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ژورنال
عنوان ژورنال: Journal of Physics: Conference Series
سال: 2006
ISSN: 1742-6588,1742-6596
DOI: 10.1088/1742-6596/42/1/015