Overpartition Theorems of the Rogers-ramanujan Type
نویسنده
چکیده
We give one-parameter overpartition-theoretic analogues of two classical families of partition identities: Andrews’ combinatorial generalization of the Gollnitz-Gordon identities and a theorem of Andrews and Santos on partitions with attached odd parts. We also discuss geometric counterparts arising from multiple q-series identities. These involve representations of overpartitions in terms of generalized Frobenius partitions.
منابع مشابه
Overpartitions, lattice paths, and Rogers-Ramanujan identities
Abstract. 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...
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