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...

• Type: Journal
• Year: 2007
• Where: JCT
• Authors: Sylvie Corteel, Olivier Mallet
• Keywords: Combinatorial, Identities, JCT 2007, Les Overpartitions