Proof of two divisibility properties of binomial coefficients conjectured by Z.-W. Sun

zbMath1305.11013arXiv1312.7548MaRDI QIDQ405269

Victor J. W. Guo

Publication date: 4 September 2014

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.7548

zbMATH Keywords

congruencesbinomial coefficients\(p\)-adic order\(q\)-Catalan numbersreciprocal and unimodal polynomials

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) (q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65)

Related Items

Unnamed Item ⋮ On some divisibility properties of binomial sums ⋮ Proof of a conjecture of Amdeberhan and Moll on a divisibility property of binomial coefficients ⋮ Unnamed Item ⋮ Proof of Sun's conjectures on integer-valued polynomials ⋮ Proof of a conjecture involving Sun polynomials

Cites Work

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• Proof of Sun's conjecture on the divisibility of certain binomial sums
• On divisibility of convolutions of central binomial coefficients
• A \(q\)-rious positivity
• q-Catalan numbers
• Catalan numbers, \(q\)-Catalan numbers and hypergeometric series
• Super ballot numbers
• On the difference of successive Gaussian polynomials
• \(t,q\)-Catalan numbers and the Hilbert scheme.
• A proof of the \(q,t\)-Catalan positivity conjecture
• Conjectured statistics for the \(q,t\)-Catalan numbers.
• The cyclic sieving phenomenon
• Products and sums divisible by central binomial coefficients
• Some divisibility properties of binomial and \(q\)-binomial coefficients
• q-Catalan Identities
• Factorial ratios, hypergeometric series, and a family of step functions
• A Theorem on Reciprocal Polynomials with Applications to Permutations and Compositions
• ON DIVISIBILITY OF BINOMIAL COEFFICIENTS