Partial-Sum Analogues of the Rogers–Ramanujan Identities
Copyright policy )Partial-Sum Analogues of the Rogers–Ramanujan Identities
A new type of polynomial analogue of the Rogers-Ramanujan identities is proven. Here the product-side of the Rogers-Ramanujan identities is replaced by a partial theta sum and the sum-side by a weighted sum over Schur polynomials.
15 pages, AMS-LaTeX
- University of Queensland Australia
- University of Melbourne Australia
- University of Queensland Australia
Combinatorial aspects of partitions of integers, Rogers-Ramanujan identities, Secondary 05A17, 17B68, \(q\)-series, q-series, Theoretical Computer Science, Primary 05A19, 33D15, Computational Theory and Mathematics, Partition identities; identities of Rogers-Ramanujan type, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Binomial coefficients; factorials; \(q\)-identities, 0102 Applied Mathematics, Primary 05A19, 33D15; Secondary 05A17, 17B68, Mathematics - Quantum Algebra, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), Combinatorial identities, bijective combinatorics, Schur polynomials
Combinatorial aspects of partitions of integers, Rogers-Ramanujan identities, Secondary 05A17, 17B68, \(q\)-series, q-series, Theoretical Computer Science, Primary 05A19, 33D15, Computational Theory and Mathematics, Partition identities; identities of Rogers-Ramanujan type, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Binomial coefficients; factorials; \(q\)-identities, 0102 Applied Mathematics, Primary 05A19, 33D15; Secondary 05A17, 17B68, Mathematics - Quantum Algebra, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), Combinatorial identities, bijective combinatorics, Schur polynomials
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