A “supernormal” partition statistic

We study a bijective map from integer partitions to the prime factorizations of integers that we call “supernorm” partition, in which multiplicities parts are mapped factors natural numbers. The supernorm is connected family maps define, suggests potential apply techniques partition theory identify and prove multiplicative properties integers. As an application “supernormal” mappings (i.e., pertaining statistic), analogue formula Kural-McDonald-Sah give arithmetic densities subsets N instead relative P like previous formulas this type; builds on works Alladi, Ono, Wagner, first third authors. then make brief pertinent analytic aspects supernorm. Finally, using table additive-multiplicative correspondences, conjecture Abelian-type specialize our main theorem other known results.