An extension to overpartitions of the Rogers-Ramanujan identities for even moduli |
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Authors: | Sylvie Corteel Olivier Mallet |
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Institution: | a LRI, CNRS et Université Paris-Sud, Bâtiment 490, 91405 Orsay Cedex, France b CNRS, LIAFA, Université Denis Diderot, 2, Place Jussieu, Case 7014, F-75251 Paris Cedex 05, France c LIAFA, Université Denis Diderot, 2, Place Jussieu, Case 7014, F-75251 Paris Cedex 05, France |
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Abstract: | We study a class of well-poised basic hypergeometric series , interpreting these series as generating functions for overpartitions defined by multiplicity conditions on the number of parts. We also show how to interpret the as generating functions for overpartitions whose successive ranks are bounded, for overpartitions that are invariant under a certain class of conjugations, and for special restricted lattice paths. We highlight the cases (a,q)→(1/q,q), (1/q,q2), and (0,q), where some of the functions become infinite products. The latter case corresponds to Bressoud's family of Rogers-Ramanujan identities for even moduli. |
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Keywords: | 11P81 05A17 33D15 |
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