Another SPT crank for the number of smallest parts in overpartitions with even smallest part

作者：Jennings Shaffer C^*

来源：Journal of Number Theory, 2015, 148: 196-203.

DOI：10.1016/j.jnt.2014.09.005

• Partitions
• Overpartitions
• Smallest parts function
• Congruences
• Ranks
• Cranks
• Bailey pairs

By using the M-2-rank of an overpartition as well as a residual crank, we give another combinatorial refinement of the congruences (spt) over bar (2)(3n) (spt) over bar (2)(3n+1) 0 (mod 3). Here (spt) over bar (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 M-2-rank of an overpartition. This congruence was previously refined using the rank of an overpartition.

• 出版日期2015-3