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05-XX Combinatorics
05Axx Enumerative combinatorics
05A30 $q$ -calculus and related topics

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Displaying 1 – 13 of 13

$q$ -analogue of a binomial coefficient congruence.

Clark, W.Edwin (1995)

International Journal of Mathematics and Mathematical Sciences

$q$ -analogues of the Hermite polynomials. (Les $q$ -analogues des polynômes d'Hermite.)

Désarménien, Jacques (1982)

Séminaire Lotharingien de Combinatoire [electronic only]

$q$ -analogues of two supercongruences of Z.-W. Sun

Cheng-Yang Gu, Victor J. W. Guo (2020)

Czechoslovak Mathematical Journal

We give several different $q$ -analogues of the following two congruences of Z.-W. Sun: $\sum_{k = 0}^{(p^{r} - 1) / 2} \frac{1}{8^{k}} (\binom{2 k}{k}) \equiv (\frac{2}{p^{r}}) (mod p^{2}) and \sum_{k = 0}^{(p^{r} - 1) / 2} \frac{1}{16^{k}} (\binom{2 k}{k}) \equiv (\frac{3}{p^{r}}) (mod p^{2}),$ where $p$ is an odd prime, $r$ is a positive integer, and $(\frac{m}{n})$ is the Jacobi symbol. The proofs of them require the use of some curious $q$ -series identities, two of which are related to Franklin’s involution on partitions into distinct parts. We also confirm a conjecture of the latter author and Zeng in 2012.

$q$ -Bernoulli numbers associated with $q$ -Stirling numbers.

Kim, Taekyun (2008)

Advances in Difference Equations [electronic only]

$q$ -exponential families.

Morrison, Kent E. (2004)

The Electronic Journal of Combinatorics [electronic only]

$q$ -extensions for the Apostol–Genocchi polynomials.

Luo, Qiuming (2009)

General Mathematics

$q$ -Genocchi numbers and polynomials associated with $q$ -Genocchi-type $l$ -functions.

Simsek, Yilmaz, Cangül, Ismail Naci, Kurt, Veli, Kim, Daeyeoul (2008)

Advances in Difference Equations [electronic only]

$q$ -identities related to overpartitions and divisor functions.

Fu, Amy M., Lascoux, Alain (2005)

The Electronic Journal of Combinatorics [electronic only]

$q$ -Riemann zeta function.

Kim, Taekyun (2004)

International Journal of Mathematics and Mathematical Sciences

$q$ -Selberg integrals and Macdonald polynomials

Jyoichi Kaneko (1996)

Annales scientifiques de l'École Normale Supérieure

q-difference equations and Ramanujan-Selberg continued fractions

Liang-Cheng Zhang (1991)

Acta Arithmetica

Qseries Maple tutorial: A $q$ -product tutorial for a $q$ -series Maple package.

Garvan, Frank (1999)

Séminaire Lotharingien de Combinatoire [electronic only]

Quintuple products and Ramanujan's partition congruence p(11n+6) ≡ 0(mod 11)

Wenchang Chu (2007)

Acta Arithmetica

Currently displaying 1 – 13 of 13

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