Cumulants, lattice paths, and orthogonal polynomials

DOI10.1016/S0012-365X(02)00834-8zbMath1026.05005arXivmath/0110031OpenAlexW3098845656MaRDI QIDQ1406554

Franz Lehner

Publication date: 4 September 2003

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0110031

zbMATH Keywords

cumulantsorthogonal polynomialscontinued fractionsMotzkin pathsLagrange inversion formulaHankel determinantslattice path combinatoricsŁukasiewicz paths

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial probability (60C05) Continued fractions and generalizations (11J70)

Related Items

COMBINATORIAL RELATION BETWEEN FREE CUMULANTS AND JACOBI PARAMETERS, Composing arbitrarily many \(SU(N)\) fundamentals, Enumerations of plane trees with multiple edges and Raney lattice paths, Bijections of Motzkin paths using shifted Riordan decompositions, Counting lattice paths with four types of steps, From generalized directed animals to the asymmetric simple exclusion process, \(\eta\)-series and a Boolean Bercovici--Pata bijection for bounded \(k\)-tuples, Cumulants and convolutions via Abel polynomials, Enumeration of lattice paths with infinite types of steps and the Chung-Feller property, Decomposition results for Gram matrix determinants

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