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05-XX Combinatorics

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$q$ -analogue of a binomial coefficient congruence.

Clark, W.Edwin (1995)

International Journal of Mathematics and Mathematical Sciences

$q$ -analogue of the Lucas congruence. (Zum $q$ -Analogon der Kongruenz von Lucas.)

Strehl, Volker (1981)

Séminaire Lotharingien de Combinatoire [electronic only]

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

Désarménien, Jacques (1982)

Séminaire Lotharingien de Combinatoire [electronic only]

$q$ -analogues of the sums of consecutive integers, squares, cubes, quarts and quints.

Schlosser, Michael (2004)

The Electronic Journal of Combinatorics [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]

$q$ -binomials and the greatest common divisor.

Slavin, Keith R. (2008)

Integers

$q$ -counting descent pairs with prescribed tops and bottoms.

Hall, John, Liese, Jeffrey, Remmel, Jeffrey B. (2009)

The Electronic Journal of Combinatorics [electronic only]

$q$ -Eulerian polynomials and polynomials with only real zeros.

Ma, Shi-Mei, Wang, Yi (2008)

The Electronic Journal of Combinatorics [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

q-Identities for Maass waveforms.

H. Cohen (1988)

Inventiones mathematicae

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

Garvan, Frank (1999)

Séminaire Lotharingien de Combinatoire [electronic only]

Quadratic Equations over Finite Fields and Class Numbers of Real Quadratic Fields.

Takashi Agoh, Toshiaki Shoji (1998)

Monatshefte für Mathematik

Quadrilateral embeddings of the conjunction of graphs

Vladimír Železník (1988)

Mathematica Slovaca

Currently displaying 1 – 20 of 52

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