On sums of figurate numbers by using techniques of poset representation theory

2008/06/16 by Agustin Moreno C, C, Agustin Moreno
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #math.NT #math.RT #msc:05A17 #msc:11D25 #msc:11D45 #msc:11D85 #msc:11E25 #msc:11P83

paper · pdf · doi:10.48550/arxiv.0806.2486

18 pages, submitted to International Journal of Number Theory

arxiv created 2008/06/16 · arxiv updated 2009/12/01

Abstract

We use representations and differentiation algorithms of posets, in order to obtain results concerning unsolved problems on figurate numbers. In particular, we present criteria for natural numbers which are the sum of three octahedral numbers, three polygonal numbers of positive rank or four cubes with two of them equal. Some identities of the Rogers-Ramanujan type involving this class of numbers are also obtained.

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