The butterfly sequence: the second difference sequence of the numbers of integer partitions with distinct parts, its pentagonal number structure, its combinatorial identities and the cyclotomic polynomials 1-x and 1+x+x^2

26 Apr 2018 Husu Cristiano

Based on the author's previous work on the Jacobi identity for twisted relative vertex operator algebras and modules and on the generating function identities for affine Lie algebras, we interpret the second difference sequence of the sequence of the number of integer partitions with distinct parts (the strict partitions) as the sequence of the strict partitions of n with at least three parts, the three largest parts consecutive, and the smallest part at least two. The name butterfly describes both the sequence's interpretation and the underlying bijection between the set of strict partitions of positive integers m with the two largest parts consecutive, and a subset of the same kind of strict partitions of m+1... (read more)

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