Dilated Floor Functions That Commute Sometimes

descriptionPublicationkeyboard_double_arrow_right Article 25 Jul 2019Publisher:California State University, Office of the ChancellorJournal:The PUMP Journal of Undergraduate Research, volume 2, pages 107-117 (issn: 2765-8724, eissn: 2576-3725,

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Authors: Kulhanek, Travis; McDonough, Joseph; Ponomarenko, Vadim;

doi: 10.46787/pump.v2i0.1916

Dilated Floor Functions That Commute Sometimes

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Abstract

We explore the dilated floor function fa(x)= ⌊ax⌋ and its commutativity with functions of the same form. A previous paper found all a and b such that fa and fb commute for all real x. In this paper, we determine all x for which the functions commute for a particular choice of a and b. We calculate the proportion of the number line on which the functions commute. We determine bounds for how far away the functions can get from commuting. We solve this fully for integer a, b and partially for real a, b.

Related Organizations

San Diego State University
United States

Keywords

Arithmetic functions; related numbers; inversion formulas, commutativity, dilated floor functions

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