Partitions with distinct evens

George E. Andrews

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

Partitions with distinct evens

George E. Andrews

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

11 Scopus citations

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.

Original language	English (US)
Title of host publication	Advances in Combinatorial Mathematics
Subtitle of host publication	Proceedings of the Waterloo Workshop in Computer Algebra 2008
Publisher	Springer Berlin Heidelberg
Pages	31-37
Number of pages	7
ISBN (Print)	9783642035616
DOIs	https://doi.org/10.1007/978-3-642-03562-3_2
State	Published - 2009

All Science Journal Classification (ASJC) codes

General Mathematics

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

Cite this

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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.",

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AB - 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.

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BT - Advances in Combinatorial Mathematics

PB - Springer Berlin Heidelberg

ER -

Partitions with distinct evens

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