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The Bailey Lattice


Affiliations
1 Pennsylvania State University, Mont Alto, United States
2 Pennsylvania State University, University Park, United States
     

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The Rogers-Ramanujan identities [5; ch. 7] are given analytically by the following formulae: (|q|<1)
1+∑qn2/(1-q)(1-q2)...(1-qn) (1.1)
=∑1/(1-q5n+1)(1-q5n+2)2
1+∑qn2+n/(1-q)(1-q2)...(1-qn) (1.2)
=∑1/(1-q5n+2)(1-q5n+3)
These are equivalent respectively to the following combinatorial identities:
The number of partitions of n into parts with difference at least 2 equals the number of partitions of n into parts congruent to ±1, modulo 5.
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  • The Bailey Lattice

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Authors

A. K. Agarwal
Pennsylvania State University, Mont Alto, United States
G. E. Andrews
Pennsylvania State University, University Park, United States
D. M. Bressoud
Pennsylvania State University, University Park, United States

Abstract


The Rogers-Ramanujan identities [5; ch. 7] are given analytically by the following formulae: (|q|<1)
1+∑qn2/(1-q)(1-q2)...(1-qn) (1.1)
=∑1/(1-q5n+1)(1-q5n+2)2
1+∑qn2+n/(1-q)(1-q2)...(1-qn) (1.2)
=∑1/(1-q5n+2)(1-q5n+3)
These are equivalent respectively to the following combinatorial identities:
The number of partitions of n into parts with difference at least 2 equals the number of partitions of n into parts congruent to ±1, modulo 5.