An Introduction to Catalan Numbers

DOI10.1007/978-3-319-22144-1zbMath1342.05002OpenAlexW4230861636MaRDI QIDQ2945863

Steven Roman

Publication date: 14 September 2015

Published in: Compact Textbooks in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-22144-1

zbMATH Keywords

binary treeantichainDyck pathlattice pathsCatalan numberssemiordersunit interval ordersnoncrossing partitionpattern avoiding permutationsordered treeDavenport-Schinzel sequencesstack-sortable permutationsparanthesizationtriangulation of convex polygon

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Other combinatorial number theory (11B75) Special sequences and polynomials (11B83) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics (05-01)

Related Items (21)

Generating functions for reciprocal Catalan-type sums: approach to linear differentiation equation and ($p$-adic) integral equations ⋮ Exact site-percolation probability on the square lattice ⋮ On Pellnomial coefficients and Pell-Catalan numbers ⋮ Integral representations of the Catalan numbers and their applications ⋮ Computational identities for extensions of some families of special numbers and polynomials ⋮ Lattice Paths and Branched Continued Fractions: An Infinite Sequence of Generalizations of the Stieltjes–Rogers and Thron–Rogers Polynomials, with Coefficientwise Hankel-Total Positivity ⋮ On powers of the Catalan number sequence ⋮ Determinant formulas of some Toeplitz-Hessenberg matrices with Catalan entries ⋮ An approximate analytic solution for the multidimensional fractional-order time and space Burger equation based on Caputo-Katugampola derivative ⋮ Catalan numbers and free distributions of mutually free multi semicircular elements ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Catalan fragile words ⋮ Optimal location of resources maximizing the total population size in logistic models ⋮ Full \(q\)-analogue for an identity of \(\lambda\)-extended Catalan numbers ⋮ New computational formulas for special numbers and polynomials derived from applying trigonometric functions to generating functions ⋮ On the logistic diffusive equation with an interior jump condition ⋮ Some new identities and inequalities for Bernoulli polynomials and numbers of higher order related to the Stirling and Catalan numbers ⋮ Exact solution of the facilitated totally asymmetric simple exclusion process ⋮ A note on Bridgeland stability conditions and Catalan numbers ⋮ Alternating convolutions of Catalan numbers

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