A bijection between strongly stable and totally symmetric partitions (2302.02505v2)

Abstract: Artinian monomial ideals in $d$ variables correspond to $d$-dimensional partitions. We define $d$-dimensional strongly stable partitions and show that they correspond to strongly stable ideals in $d$ variables. We show a bijection between strongly stable partitions and totally symmetric partitions which preserves the side length of the minimal bounding box.