Geodesic
Labeled factorization of integers
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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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.
DOI : 10.37236/139
Classification : 11Y05, 05A18, 11B73, 05A19 
@article{10_37236_139,
     author = {Augustine O. Munagi},
     title = {Labeled factorization of integers},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/139},
     zbl = {1223.11150},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/139/}
}
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Augustine O. Munagi. Labeled factorization of integers. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/139

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