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

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.

13 pages

References in corpus (1)

• The number of simultaneous core partitions

Cited by in corpus (1)

• Symmetry in maximal $(s-1,s+1)$ cores