Multiplicative complements I
Anett Kocsis, D\'avid Matolcsi, Csaba S\'andor, Gy\"orgy, T\H{o}t\H{o}s
TL;DR
This paper investigates the density of multiplicative bases of order h for positive integers, introducing the concept of multiplicative complements and establishing tight bounds on their density.
Contribution
It introduces the notion of multiplicative complements and provides improved, tight density bounds for multiplicative bases of order h.
Findings
Established new upper bounds on the density of multiplicative bases.
Introduced the concept of multiplicative complements.
Improved previous results on the density of such bases.
Abstract
In this paper, we study how dense a multiplicative basis of order for can be, improving on earlier results. Upon introducing the notion of a \textit{multiplicative complement}, we present some tight density bounds.
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Taxonomy
TopicsRings, Modules, and Algebras · Finite Group Theory Research · Advanced Topology and Set Theory