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

JOURNAL OF NUMBER THEORY

卷:148

Article

Jennings-Shaffer, C.

关键词: Partitions;    Overpartitions;    Smallest parts function;    Congruences;    Ranks;    Cranks;    Bailey pairs;   

DOI  :  10.1016/j.jnt.2014.09.005

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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