Overpartition pairs

Lovejoy, Jeremy

Annales de l'Institut Fourier, Tome 56 (2006) no. 3, pp. 781-794.

Une paire de surpartitions est un objet combinatoire lié à l’identité $q$-Gauss et la somme ${}_1{\psi }_1$. Nous prouvons ici des identités pour certaines paires de surpartitions en utilisant la théorie des récurrences pour les séries basiques hypergéométriques (d’après Andrews) ainsi que la théorie des chaînes de Bailey.

An overpartition pair is a combinatorial object associated with the $q$-Gauss identity and the ${}_1{\psi }_1$ summation. In this paper, we prove identities for certain restricted overpartition pairs using Andrews’ theory of recurrences for well-poised basic hypergeometric series and the theory of Bailey chains.

Classification : 11P81, 33D15
Keywords: Partitions, overpartitions, basic hypergeometric series, Bailey chains
Mot clés : partitions, surpartitions, séries basiques hypergéométriques, chaînes de Bailey

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