Combinatorial Telescoping for an Identity of Andrews on Parity in Partitions

William Y.C. Chen, Daniel K. Du and Charles B. Mei

  Abstract:  Recently Andrews proposed a problem of finding a combinatorial proof of an identity on the q-little Jacobi polynomials. We give a classification of certain triples of partitions and find bijections based on this classification. By the method of combinatorial telescoping for identities on sums of positive terms, we establish a recurrence relation that leads to the identity of Andrews.

  AMS Classification:  05A17, 11P83

  Keywords:  creative telescoping, combinatorial telescoping, partition, q-little Jacobi polynomial

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