Characteristic, Counting, and Representation Functions Characterized

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Given a set A of natural numbers, i.e., nonnegative integers, there are three distinctive functions attached to it, each of which completely determines A. These are the characteristic function χA(n) which is equal to 1 or 0 according as the natural number n lies or does not lie in A, the counting function A(n) which gives the number of elements a of A satisfying a ≤ n, and the representation function rA(n) which counts the ordered pairs (a, b) of elements a, b ∈ A such that a + b = n. We establish direct relations between these three functions. In particular, we express each one of them in terms of each other one. We also characterize the representation functions by an intrinsic recursive relation which is a necessary and sufficient condition.

Original languageEnglish (US)
Title of host publicationCombinatorial and Additive Number Theory II - CANT
EditorsMelvyn B. Nathanson
PublisherSpringer New York LLC
Pages139-155
Number of pages17
ISBN (Print)9783319680309
DOIs
StatePublished - Jan 1 2017
Event13th Workshop on Combinatorial and Additive Number Theory, CANT 2015 - New York, United States
Duration: May 19 2015May 22 2015

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume220
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other13th Workshop on Combinatorial and Additive Number Theory, CANT 2015
CountryUnited States
CityNew York
Period5/19/155/22/15

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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