Supernomial Coefficients,Polynomial Identities and q-Series |
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Authors: | Schilling Anne Warnaar S Ole |
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Institution: | (1) Institute for Theoretical Physics, State University of New York, Stony Brook, New York, 11794-3840. E-mail;(2) Department of Mathematics, University of Melbourne, Parkville, Victoria, 3052, Australia. E-mail |
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Abstract: | q-Analogues of the coefficients of xa in the expansion of
j=1
N
(1 + x + + xj)Lj are proposed. Useful properties, such as recursion relations, symmetries and limiting theorems of the q-supernomial coefficients are derived, and a combinatorial interpretation using generalized Durfee dissection partitions is given. Polynomial identities of boson-fermion-type, based on the continued fraction expansion of p/k and involving the q-supernomial coefficients, are proven. These include polynomial analogues of the Andrews-Gordon identities. Our identities unify and extend many of the known boson-fermion identities for one-dimensional configuration sums of solvable lattice models, by introducing multiple finitization parameters. |
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Keywords: | polynomial identities Rogers-Ramanujan type identities q-series |
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