Schilling, Anne; Warnaar, S. Ole Supernomial coefficients, polynomial identities and \(q\)-series. (English) Zbl 0921.05007 Ramanujan J. 2, No. 4, 459-494 (1998). Authors’ abstract: \(q\)-analogues of the coefficient of \(x^a\) in the expansion of \(\prod^N_{j=1} (1+x+x^2+ \cdots+ x^j)^{L_j}\) are proposed. Useful properties, such as recursion relations, symmetries and limiting theorems of the “\(q\)-supernomial coefficients” 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 given. 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 known lattice models by introducing multiple finitization parameters. Reviewer: H. N. V. Temperley (Langport) Cited in 15 Documents MSC: 05A30 \(q\)-calculus and related topics 05A19 Combinatorial identities, bijective combinatorics 11P84 Partition identities; identities of Rogers-Ramanujan type 33E99 Other special functions 82B23 Exactly solvable models; Bethe ansatz Keywords:\(q\)-supernomial coefficients; Durfee dissection partitions; continued-fraction expansion; Andrews-Gordon identities; boson-fermion identities PDFBibTeX XMLCite \textit{A. Schilling} and \textit{S. O. Warnaar}, Ramanujan J. 2, No. 4, 459--494 (1998; Zbl 0921.05007) Full Text: DOI arXiv