Partitions With Distinct Evens

George E. Andrews ()
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George E. Andrews: The Pennsylvania State University, Department of Mathematics

Chapter Chapter 2 in Advances in Combinatorial Mathematics, 2009, pp 31-37 from Springer

Abstract: Abstract Partitions with no repeated even parts (DE-partitions) are considered. A DE-rank for DE-partitions is defined to be the integer part of half the largest part minus the number of even parts. Δ(n) denotes the excess of the number of DE-partitions with even DE-rank over those with odd DE-rank. Surprisingly Δ(n) is (1) always non-negative, (2) almost always zero, and (3) assumes every positive integer value infinitely often. The main results follow from the work of Corson, Favero, Liesinger and Zubairy. Companion theorems for DE-partitions counted by exceptional parts conclude the paper.

Keywords: Companion Theorem; Mock Theta Function; Basic Hypergeometric Series; Legendre Symbol; Lacunary Series (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-03562-3_2

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DOI: 10.1007/978-3-642-03562-3_2

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