Overpartitions, lattice paths and Rogers-Ramanujan identities

Sylvie Corteel (1) , Olivier Mallet (2)

1 LRI - Laboratoire de Recherche en Informatique
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

We extend partition-theoretic work of Andrews, Bressoud, and Burge to overpartitions, defining the notions of successive ranks, generalized Durfee squares, and generalized lattice paths, and then relating these to overpartitions defined by multiplicity conditions on the parts. This leads to many new partition and overpartition identities, and provides a unification of a number of well-known identities of the Rogers-Ramanujan type. Among these are Gordon's generalization of the Rogers-Ramanujan identities, Andrews' generalization of the Göllnitz-Gordon identities, and Lovejoy's ``Gordon's theorems for overpartitions."

Mots clés: Partitions; overpartitions; Rogers-Ramanujan identities; lattice paths

Domaines: Combinatoire [math.CO]

Sylvie Corteel, Olivier Mallet. Overpartitions, lattice paths and Rogers-Ramanujan identities. 2006. ⟨hal-00017295v2⟩