Supernomial coefficients, polynomial identities and q-series
نویسندگان
چکیده
q-Analogues of the coefficients of x in the expansion of ∏N j=1(1 + x + · · · + x )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.
منابع مشابه
Supernomial Coefficients , Bailey ’ S Lemma and Rogers – Ramanujan - Type Identities
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