A combinatorial proof of the Rogers-Ramanujan and Schur identities

Details A combinatorial proof of the Rogers-Ramanujan and Schur identities A combinatorial proof of the Rogers-Ramanujan and Schur identities

2004-11-03

arxiv.org/abs/math/0411072v2

Mathematics

Combinatorics

12 pages, 5 figures; incorporated referee suggestions, simplified definition of (k,m)-rank, to appear in JCT(A)

Scientific paper

We give a combinatorial proof of the first Rogers-Ramanujan identity by using
two symmetries of a new generalization of Dyson's rank. These symmetries are
established by direct bijections.

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