The Method of Combinatorial Telescoping

William Y.C. Chen, Qing-Hu Hou, and Lisa H. Sun

  Abstract:  We present a method for proving q-series identities by combinatorial telescoping, in the sense that one can transform a bijection or a classification of combinatorial objects into a telescoping relation. We shall illustrate this method by giving a combinatorial proof of Watson's identity. The latter implies the Rogers-Ramanujan identities.

  AMS Classification:  05A17; 11P83

  Keywords:  Watson's identity, Sylvester's identity, Rogers-Ramanujan identities, combinatorial telescoping

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