Titlebook: Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra; In Honour of Peter P Veronika Pillwein,Carste

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Refined ,-Trinomial Coefficients and Two Infinite Hierarchies of ,-Series Identities,al identities using transformation properties of the refined .-trinomials in an iterative fashion in the spirit of Bailey chains. One of these two hierarchies contains an identity which is equivalent to Capparelli’s first Partition Theorem.

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,An Eigenvalue Problem for the Associated Askey–Wilson Polynomials,e associated Askey–Wilson polynomials introduced by Ismail and Rahman. The Askey–Wilson operator, applied in each variable separately, maps this function to the ordinary Askey–Wilson polynomials with different sets of parameters. A third Askey–Wilson operator is found with the help of a computer alg

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Context-Free Grammars and Stable Multivariate Polynomials over Stirling Permutations,rves as a unification of the results of Bóna, Brenti, Janson, Kuba, and Panholzer. Let .(.) be the generating polynomials of the descent statistic over Legendre-Stirling permutations, and let .(.) = 2.(.∕2), where .(.) are the second-order Eulerian polynomials. Haglund and Visontai proposed the prob

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Difference Equation Theory Meets Mathematical Finance,cations of Pringsheim’s theorem and two applications of the saddle point method. In this paper, we add a section on Hankel contour asymptotics. This method is well-known in analytic combinatorics from Flajolet and Odlyzko’s singularity analysis of generating functions, and is applied here to a probl

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Evaluations as ,-Subsets,0, 1}. But in “Applied Mathematics” multivalued parameters are used. For example, if a given refrigerant is ecologically worthwhile may be answered by its values of ODP (ozone depletion potential), GWP (general warming potential) and ALT (atmospheric lifetime), i.e. by a triple of real numbers. Let

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Exact Lower Bounds for Monochromatic Schur Triples and Generalizations,}, subject to a coloring with two different colors. Previously, only asymptotic formulas for such bounds were known, and only for .. Using symbolic computation techniques, these results are extended here to arbitrary .. Furthermore, we give exact formulas for the minimum number of monochromatic Schu

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Untying the Gordian Knot via Experimental Mathematics,before us, the simple, “cheating” solution to a hard problem is the best. So before you spend days (and possibly years) trying to answer a mathematical question by analyzing and trying to ‘understand’ its structure, let your computer generate enough data, and then let it guess the answer. Often its