TL;DR
This paper investigates the enumeration of factorizations of positive integers with parts colored in l different ways, providing formulas for various cases including ordered, unordered, distinct, and non-distinct factorizations.
Contribution
It introduces recursive and explicit formulas for counting factorizations with multiple colors across different ordering and distinctness scenarios.
Findings
Derived formulas for unordered and ordered factorizations with l colors.
Extended results to both distinct and non-distinct factorizations.
Provided comprehensive methods for counting colored factorizations.
Abstract
We study the number of factorizations of a positive integer, where the parts of the factorization are of l different colors (or kinds). Recursive or explicit formulas are derived for the case of unordered and ordered, distinct and non-distinct factorizations with at most and exactly l colors.
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Taxonomy
Topicsgraph theory and CDMA systems · Advanced Mathematical Identities · Analytic Number Theory Research