Symmetry in maximal $(s-1,s+1)$ cores
Combinatorics
2014-11-04 v1
Abstract
We explain a "curious symmetry" for maximal -core partitions first observed by T. Amdeberhan and E. Leven. Specifically, using the -abacus, we show such partitions have empty -core and that their -quotient is comprised of 2-cores. This imposes strong conditions on the partition structure, and implies both the Amdeberhan-Leven result and additional symmetry. We also find a more general family that exhibits these symmetries.
Cite
@article{arxiv.1411.0339,
title = {Symmetry in maximal $(s-1,s+1)$ cores},
author = {Rishi Nath},
journal= {arXiv preprint arXiv:1411.0339},
year = {2014}
}