Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593661 | Journal of Number Theory | 2015 | 8 Pages |
Abstract
By using the M2-rank of an overpartition as well as a residual crank, we give another combinatorial refinement of the congruences spt¯2(3n)â¡spt¯2(3n+1)â¡0(mod3). Here spt¯2(n) is the total number of appearances of the smallest parts among the overpartitions of n where the smallest part is even and not overlined. Our proof depends on Bailey's Lemma and the rank difference formulas of Lovejoy and Osburn for the M2-rank of an overpartition. This congruence was previously refined using the rank of an overpartition.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
C. Jennings-Shaffer,