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{\bf Augustine O. Munagi}
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{\bf Labeled Factorization of Integers}
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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
of complementing subsets of $\{0,1,\dots,n-1\}$. We also give a new
combinatorial interpretation of a class of generalized Stirling
numbers.



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