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Titlebook: Lattice Path Combinatorics and Applications; George E. Andrews,Christian Krattenthaler,Alan Kri Book 2019 Springer Nature Switzerland AG 2

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Asymptotic Behaviour of Certain ,-Poisson, ,-Binomial and Negative ,-Binomial Distributions,med continuous Stieltjes–Wigert distribution and that of the Euler distribution to a deformed Gaussian distribution are established. Note that the Heine distribution is the limiting behaviour of both the .-binomial distribution of the first kind (.-Binomial I) and the negative .-binomial distributio
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Paired Patterns in Lattice Paths,ll words . with . .’s and . .’s. Given . and a subset . of ., we let . denote the word that results from . by removing the . occurrence of . and the . occurrence of . in . for all ., reading from left to right. Then, we say that a paired pattern . occurs in . if there is some . of size . such that .
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Explicit Formulas for Enumeration of Lattice Paths: Basketball and the Kernel Method,d kernel method, leads to explicit formulas for the number of walks of length ., for any ., in terms of nested sums of binomials. We finally relate some special cases to other combinatorial problems, or to problems arising in queuing theory.
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