dorsal/arxiv
View SchemaSupernomial coefficients, polynomial identities and $q$-series
| Authors | Anne Schilling, S. Ole Warnaar |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9701007 |
| URL | https://arxiv.org/abs/q-alg/9701007 |
| Journal | The Ramanujan Journal 2 (1998) 459-494 |
Abstract
$q$-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.
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"abstract": "$q$-Analogues of the coefficients of $x^a$ in the expansion of $\\prod_{j=1}^N\n(1+x+...+x^j)^{L_j}$ are proposed. Useful properties, such as recursion\nrelations, symmetries and limiting theorems of the ``$q$-supernomial\ncoefficients\u0027\u0027 are derived, and a combinatorial interpretation using\ngeneralized Durfee dissection partitions is given. Polynomial identities of\nboson-fermion-type, based on the continued fraction expansion of $p/k$ and\ninvolving the $q$-supernomial coefficients, are proven. These include\npolynomial analogues of the Andrews-Gordon identities. Our identities unify and\nextend many of the known boson-fermion identities for one-dimensional\nconfiguration sums of solvable lattice models, by introducing multiple\nfinitization parameters.",
"arxiv_id": "q-alg/9701007",
"authors": [
"Anne Schilling",
"S. Ole Warnaar"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"journal_ref": "The Ramanujan Journal 2 (1998) 459-494",
"title": "Supernomial coefficients, polynomial identities and $q$-series",
"url": "https://arxiv.org/abs/q-alg/9701007"
},
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