Characterizing the supernorm partition statistic

Abstract The paper gives characterizations of the supernorm statistic $$\widehat{N} :\mathcal {P}\rightarrow \mathbb {N}^{+}$$ N ^ : P → + for partitions, where $$\mathcal {P}$$ is set integer partitions and $$\mathbb positive integers. map a bijection onto that defines total order on ordering, obtained by pulling back additive . ordering refines two partial orders partitions: multiset inclusion order, whose image under $$\widehat{N}$$ divisibility lattice , Young’s order. shows it characterized these properties, additionally with requirement an order-isomorphism from to It also mapping exactly one part bijectively prime numbers. presents construction showing latter additional conditions are necessary characterization hold.