English

Two truncated identities of Gauss

Combinatorics 2013-01-15 v2 Number Theory

Abstract

Two new expansions for partial sums of Gauss' triangular and square numbers series are given. As a consequence, we derive a family of inequalities for the overpartition function pˉ(n)\bar{p}(n) and for the partition function p1(n)p_1(n) counting the partitions of nn with distinct odd parts. Some further inequalities for variations of partition function are proposed as conjectures.

Keywords

Cite

@article{arxiv.1205.4340,
  title  = {Two truncated identities of Gauss},
  author = {Victor J. W. Guo and Jiang Zeng},
  journal= {arXiv preprint arXiv:1205.4340},
  year   = {2013}
}

Comments

9 pages, final version