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|
|Number of pages||7|
|State||Published - Dec 1 2009|
All Science Journal Classification (ASJC) codes