Ballot matrix as Catalan matrix power and related identities

DOI10.1016/j.dam.2011.10.016zbMath1236.05018OpenAlexW1993685878MaRDI QIDQ765378

Stefan Stanimirović, Predrag S. Stanimirović, Aleksandar Ilić

Publication date: 19 March 2012

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

Full work available at URL: https://doi.org/10.1016/j.dam.2011.10.016

zbMATH Keywords

Catalan numbergenerating functiongeneralized hypergeometric functionCatalan matrixBallot matrixBallot number

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65) Classical hypergeometric functions, ({}_2F_1) (33C05) Matrices of integers (15B36)

Related Items (6)

Fuss-Catalan matrices, their weighted sums, and stabilizer subgroups of the Riordan group ⋮ Schröder matrix as inverse of Delannoy matrix ⋮ The cyclic groups generated by Catalan matrices ⋮ Some inverse relations determined by Catalan matrices ⋮ Proofs of two conjectures on Catalan triangle numbers ⋮ A unified approach for the Catalan matrices by using Riordan arrays

Cites Work

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• Catalan matrix and related combinatorial identities
• The Lucas matrix and some combinatorial identities
• Identities via Bell matrix and Fibonacci matrix
• Moments on Catalan numbers
• Factors of binomial sums from the Catalan triangle
• Catalan numbers, their generalization, and their uses
• Super ballot numbers
• A Catalan triangle
• Pascal triangles, Catalan numbers and renewal arrays
• Some combinatorial identities via Fibonacci numbers
• Factorial ratios that are integers.
• Exponential sums with Catalan numbers and middle binomial coefficients
• Enumeration via ballot numbers
• A factorization of the symmetric Pascal matrix involving the Fibonacci matrix
• New identities in the Catalan triangle
• Bernoulli matrix and its algebraic properties
• ON THE (n, k)-TH CATALAN NUMBERS
• Pascal's Matrices
• Stirling matrix via Pascal matrix
• The linear algebra of the generalized Pascal matrix
• Inverting linear combinations of identity and generalized Catalan matrices

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