q-Catalan Identities

DOI10.1007/978-1-4419-6263-8_10zbMath1322.11018OpenAlexW181580364MaRDI QIDQ3193074

George E. Andrews

Publication date: 14 October 2015

Published in: The Legacy of Alladi Ramakrishnan in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4419-6263-8_10

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) (q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Asymptotic enumeration (05A16)

Related Items

Some congruences on \(q\)-Catalan numbers, Refined Catalan and Narayana cyclic sieving, New proofs of two $q$-analogues of Koshy’s formula, Identities on extended Catalan numbers and their \(q\)-analogs, Some divisibility properties of binomial and \(q\)-binomial coefficients, Fast computation of the \(N\)-th term of a \(q\)-holonomic sequence and applications, Proof of two divisibility properties of binomial coefficients conjectured by Z.-W. Sun, Several identities and relations related to \(q\)-analogues of Pochhammer \(k\)-symbol with applications to Fuss-Catalan-Qi numbers, Narayana polynomials and Hall-Littlewood symmetric functions, Congruences from $q$-Catalan Identities, Full \(q\)-analogue for an identity of \(\lambda\)-extended Catalan numbers, Several formulas and identities related to Catalan-Qi and \(q\)-Catalan-Qi numbers, Identities from representation theory, Touchard type identity for \(q\)-Narayana numbers, Lattice paths and the \(q\)-ballot polynomials

Cites Work

• q-Catalan numbers
• Catalan numbers, \(q\)-Catalan numbers and hypergeometric series
• On the difference of successive Gaussian polynomials
• Applications of Basic Hypergeometric Functions
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