Supernomial coefficients, polynomial identities and $q$-series

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dc.creatorSchilling, Anne
dc.creatorWarnaar, S. Ole
dc.date1997-01-08
dc.date1998-02-23
dc.date.accessioned2026-07-07T09:08:44Z
dc.date.available2026-07-07T09:08:44Z
dc.description$q$-Analogues of the coefficients of $x^a$ in the expansion of $\prod_{j=1}^N (1+x+...+x^j)^{L_j}$ 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.
dc.description34 pages, Latex2e, figures; improved version
dc.identifierhttps://arxiv.org/abs/q-alg/9701007
dc.identifierhttp://arxiv.org/abs/q-alg/9701007
dc.identifierThe Ramanujan Journal 2 (1998) 459-494
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150829
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.titleSupernomial coefficients, polynomial identities and $q$-series
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