Overpartitions, lattice paths, and Rogers-Ramanujan identities

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Overpartitions, lattice paths, and Rogers-Ramanujan identities
We define the notions of successive ranks and generalized Durfee squares for overpartitions. We show how these combinatorial statistics give extensions to overpartitions of combinatorial interpretations in terms of lattice paths of the generalizations of the Rogers-Ramanujan identities due to Burge, Andrews and Bressoud. All our proofs are combinatorial and use bijective techniques. Our result includes the Andrews-Gordon identities, the generalization of the Gordon-G¨ollnitz identities and Gordon’s theorems for overpartitions. R´esum´e. Nous d´efinissons les notions de rangs successifs et de carr´e de Durfee g´en´eralis´e pour les overpartitions. Nous montrons comment ces statistiques combinatoires permettent d’´etendre aux overpartitions des interpr´etations combinatoires en termes de chemins des g´en´eralisations des identit´es de Rogers-Ramanujan dues `a Burge, Andrews et Bressoud. Toutes nos preuves sont combinatoires et utilisent des techniques bijectives. Notre...
Sylvie Corteel, Olivier Mallet
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2007
Where JCT
Authors Sylvie Corteel, Olivier Mallet
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