A short Rogers-Ramanujan bijection (Q1160180)
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scientific article; zbMATH DE number 3747129
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A short Rogers-Ramanujan bijection |
scientific article; zbMATH DE number 3747129 |
Statements
A short Rogers-Ramanujan bijection (English)
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1982
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Recently \textit{A. M. Garsia} and \textit{S. C. Milne} [Proc. Natl. Acad. Sci. USA 78, 2026--2028 (1981; Zbl 0464.05007)] proved the Rogers-Ramanujan identity by presenting a bijection between \(C(n)\) the number of partitions of \(n\) with parts \(\equiv 1, 4 \pmod 5\) and \(A(n)\) the number of partitions of \(n\) with minimal difference \(2\). The authors present another bijective proof which is similar to that of Garsia and Milne. It involves an iteration of two involutions one of which is equivalent to the Jacobi triple product identity, while the other is considerably simpler than that of Garsia and Milne.
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Rogers-Ramanujan identity
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bijective proof
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involutions
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