On the largest size of $(t,t+1,..., t+p)$-core partitions

Huan Xiong

On the largest size of $(t,t+1,..., t+p)$-core partitions

Combinatorics 2015-01-08 v2

Authors: Huan Xiong

Abstract

In this paper we prove that Amdeberhan's conjecture on the largest size of $(t, t+1, t+2)$ -core partitions is true. We also show that the number of $(t, t + 1, t + 2)$ -core partitions with the largest size is $1$ or $2$ based on the parity of $t$ . More generally, the largest size of $(t,t+1,..., t+p)$ -core partitions and the number of such partitions with the largest size are determined.

Keywords

core partitions largest size Amdeberhan conjecture combinatorics partition theory

Cite

@article{arxiv.1410.2061,
  title  = {On the largest size of $(t,t+1,..., t+p)$-core partitions},
  author = {Huan Xiong},
  journal= {arXiv preprint arXiv:1410.2061},
  year   = {2015}
}

Comments

13 pages

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