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Rank and Conjugation for the Frobenius Representation of an Overpartition
Jeremy Lovejoy
CNRS, LIAFA, Universit Denis Diderot, Case 7014, 2 Place Jussieu, F-75251 Paris Cedex 05 France
lovejoy@liafa.jussieu.fr
Annals of Combinatorics 9 (3) p.321-334 September, 2005
AMS Subject Classification: 11P81, 05A17
Abstract:
We discuss conjugation and Dyson's rank for overpartitions from the perspective of the Frobenius representation. More specifically, we translate the classical definition of Dyson's rank to the Frobenius representation of an overpartition and define a new kind of conjugation in terms of this representation. We then use q-series identities to study overpartitions that are self-conjugate with respect to this conjugation.
Keywords: partitions, overpartitions, Frobenius partitions, Dyson's rank, conjugation

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