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Self-conjugate vector partitions and the parity of the spt-function

George E. Andrews, Frank G. Garvan, Jie Liang (2013)

Acta Arithmetica

Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. Recently, we found new combinatorial interpretations of congruences for the spt-function modulo 5 and 7. These interpretations were in terms of a restricted set of weighted vector partitions which we call S-partitions. We prove that the number of self-conjugate S-partitions, counted with a certain weight, is related to the coefficients of a certain mock theta function studied by the first author,...

Séries de $q$ -factorielles, opérateurs aux $q$ -différences et confluence

Anne Duval (2003)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Several $q$ -series identities from the Euler expansions of ${(a; q)}_{\infty}$ and $\frac{1}{{(a; q)}_{\infty}}$

Zhizheng Zhang, Yang, Jizhen (2009)

Archivum Mathematicum

In this paper, we first give several operator identities which extend the results of Chen and Liu, then make use of them to two $q$ -series identities obtained by the Euler expansions of ${(a; q)}_{\infty}$ and $\frac{1}{{(a; q)}_{\infty}}$ . Several $q$ -series identities are obtained involving a $q$ -series identity in Ramanujan’s Lost Notebook.

Signed words and permutations. III: The MacMahon Verfahren.

Foata, Dominique, Han, Guo-Niu (2005)

Séminaire Lotharingien de Combinatoire [electronic only]

Some explicit values for ratios of theta-functions.

Mahadeva Naika, M.S., Madhusudhan, H.S. (2005)

General Mathematics

Some new transformations for Bailey pairs and WP-Bailey pairs

James Mc Laughlin (2010)

Open Mathematics

We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions which can also be expressed as certain types of Lambert series.

Some recurrence relations for the generalized basic hypergeometric functions.

Purohit, S.D. (2009)

Bulletin of Mathematical Analysis and Applications [electronic only]

Some relationships between the analogs of Euler numbers and polynomials.

Ryoo, C.S., Kim, T., Jang, Lee-Chae (2007)

Journal of Inequalities and Applications [electronic only]

Some theorems on the explicit evaluations of singular moduli.

Bairy, K. Sushan (2009)

General Mathematics

Supernomial coefficients, supernomials coefficients Bailey's lemma and Rogers-Ramanujan-type identities. A survey of results and open problems.

Warnaar, S.Ole (1999)

Séminaire Lotharingien de Combinatoire [electronic only]

Systèmes aux $q$ -différences singuliers réguliers : classification, matrice de connexion et monodromie

Jacques Sauloy (2000)

Annales de l'institut Fourier

G.D. Birkhoff a posé, par analogie avec le cas classique des équations différentielles, le problème de Riemann-Hilbert pour les systèmes “fuchsiens” aux $q$ -différences linéaires, à coefficients rationnels. Il l’a résolu dans le cas générique: l’objet classifiant qu’il introduit est constitué de la matrice de connexion $P$ et des exposants en $0$ et $\infty$ . Nous reprenons sa méthode dans le cas général, mais en traitant symétriquement $0$ et $\infty$ et sans recours à des solutions à croissance “sauvage”. Lorsque $q$ ...

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