An integration of Euler's pentagonal partition

Details An integration of Euler's pentagonal partition An integration of Euler's pentagonal partition

2010-09-19

arxiv.org/abs/1009.3645v1

Mathematics

Combinatorics

22 pages, 2 figures. The recurrence investigated in this paper is essentially that proposed in Exercise 5.2.3 of Igor Pak's "P

Scientific paper

A recurrent formula is presented, for the enumeration of the compositions of positive integers as sums over multisets of positive integers, that closely resembles Euler's recurrence based on the pentagonal numbers, but where the coefficients result from a discrete integration of Euler's coefficients. Both a bijective proof and one based on generating functions show the equivalence of the subject recurrences.

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