Let s be even and greater than 2. We explain a “curious symmetry” for maximal (s? 1, s+ 1)-core partitions first observed by T. Amdeberhan and E. Leven. Specifically, using the s-abacus, we show such partitions have empty s-core and that their squotient is comprised of 2-cores. These conditions impose strong conditions on the partition structure, and imply both the Amdeberhan-Leven result and additional symmetry. We conclude by finding the most general family of partitions that exhibit these symmetries, and obtain some new results on maximal (s ? 1, s, s + 1)-core partitions.
展开▼
