Year: 2014
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Xiong, Huan
Institution: University of Zurich
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952090830