Factors of the Gaussian coefficients

DOI10.1016/j.disc.2006.03.031zbMath1096.05008OpenAlexW1975647698MaRDI QIDQ2497483

William Y. C. Chen, Qing-Hu Hou

Publication date: 4 August 2006

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

Full work available at URL: https://doi.org/10.1016/j.disc.2006.03.031

zbMATH Keywords

\(q\)-multinomial coefficient\(q\)-Catalan numbercyclotomic polynomialGaussian coefficient

Mathematics Subject Classification ID

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

Related Items (17)

Unnamed Item ⋮ q-Analogues of some supercongruences related to Euler numbers ⋮ A note on affine cones over Grassmannians and their stringy 𝐸-functions ⋮ On a generalization of a congruence related to \(q\)-Narayana numbers ⋮ A \(q\)-analogue of a Ramanujan-type supercongruence involving central binomial coefficients ⋮ Proof of some supercongruences through a \(q\)-microscope ⋮ Cores and independence numbers of Grassmann graphs ⋮ \(q\)-analogs of some congruences involving Catalan numbers ⋮ Factors of sums and alternating sums of products of \(q\)-binomial coefficients and powers of \(q\)-integers ⋮ Mahonian pairs ⋮ Divisibility of some binomial sums ⋮ Factors of alternating binomial sums ⋮ Proof of a supercongruence conjectured by Sun through a \(q\)-microscope ⋮ Proofs of two conjectures on Catalan triangle numbers ⋮ Factors of certain sums involving central \(q\)-binomial coefficients ⋮ Some variations of a ‘divergent’ Ramanujan-type q-supercongruence ⋮ Some congruences related to the q-Fermat quotients

Cites Work

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• On the polynomial \(\frac {1} {[n_q}[ ^n_k]_q\)]
• Arithmetic properties of generalized Euler numbers
• Some arithmetic properties of the \(q\)-Euler numbers and \(q\)-Salié numbers
• Applications of q-Lagrange Inversion to Basic Hypergeometric Series
• A New q-Lagrange Formula and some Applications
• The power of a prime that divides a generalized binomial coefficient.
• Further Divisibility Properties of the q-Tangent Numbers
• Divisibility Properties of the q-Tangent Numbers
• Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients

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