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Labeled Factorization of Integers
Electronic Journal of Combinatorics
The labeled factorizations of a positive integer $n$ are obtained as a completion of the set of ordered factorizations of $n$. This follows a new technique for generating ordered factorizations found by extending a method for unordered factorizations that relies on partitioning the multiset of prime factors of $n$. Our results include explicit enumeration formulas and some combinatorial identities. It is proved that labeled factorizations of $n$ are equinumerous with the systems ofdoi:10.37236/139 fatcat:hvrvabflyvem3fskuqfrfry5wu