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