Ordered Factorizations with k Factors

2016/10/16 by Jacob Sprittulla, Sprittulla, Jacob · 1 citation
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1610.04826

openalex publication_date 2016/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an overview of combinatoric properties of the number of ordered k-factorizations f_k(n,l) of an integer, where every factor is greater or equal to l. We show that for a large number k of factors, the value of the cumulative sum F_k(x,l)=∑\nolimits_{n≤ x} f_k(n,l) is a polynomial in \lfloor log_l x \rfloor and give explicit expressions for the degree and the coefficients of this polynomial. An average order of the number of ordered factorizations for a fixed number k of factors greater or equal to 2 is derived from known results of the divisor problem.

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