Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2022; 59(6): 1339-1348

Online first article November 10, 2022      Printed November 30, 2022

https://doi.org/10.4134/BKMS.b210262

Copyright © The Korean Mathematical Society.

Some remarks on problems of subset sum

Min Tang, Hongwei Xu

Anhui Normal University; Anhui Normal University

Abstract

Let $A=\{a_1<a_2<\cdots\}$ be a sequence of integers and let $P(A)=\left\{\sum \varepsilon_ia_i: a_i\in A, \varepsilon_i=0\text{ or }1, \sum \varepsilon_i<\infty\right\}$. Burr posed the following question: Determine conditions on integers sequence $B$ that imply either the existence or the non-existence of $A$ for which $P(A)$ is the set of all non-negative integers not in $B$. In this paper, we focus on some problems of subset sum related to Burr's question.

Keywords: Subset sum, complement, Burr's problem

MSC numbers: Primary 11B13

Supported by: This work was supported by the National Natural Science Foundation of China(Grant No. 11971033) and top talents project of Anhui Department of Education(Grant No. gxbjZD05).