2011/06/15 by William Y.C. Chen, Daniel K. Du, Chen, William Y. C. +4
Mathematics · #05A17 #11P83 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1106.3013
openalex publication_date 2011/06/15 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
Following the method of combinatorial telescoping for alternating sums given\nby Chen, Hou and Mu, we present a combinatorial telescoping approach to\npartition identities on sums of positive terms. By giving a classification of\nthe combinatorial objects corresponding to a sum of positive terms, we\nestablish bijections that lead a telescoping relation. We illustrate this idea\nby giving a combinatorial telescoping relation for a classical identity of\nMacMahon. Recently, Andrews posed a problem of finding a combinatorial proof of\nan identity on the q-little Jacobi polynomials which was derived based on a\nrecurrence relation. We find a combinatorial classification of certain triples\nof partitions and a sequence of bijections. By the method of cancelation, we\nsee that there exists an involution for a recurrence relation that implies the\nidentity of Andrews.\n