A Sumset Version of a Conjecture of Pilz

SIAM Journal on Discrete Mathematics 2026 Open access

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Authors: János Nagy, Péter Pál Pach
DOI: 10.1137/24m1654609
Cited by: 0

Abstract

Abstract. Pilz’s conjecture states that for any finite set [Formula: see text] of positive integers and positive integer [Formula: see text] in the union of the sets [Formula: see text] (considered as a multiset) at least [Formula: see text] values appear an odd number of times. In this short note we consider a variant of this problem. Namely, we show that in the sumset [Formula: see text] (considered as a multiset) at least [Formula: see text] values appear an odd number of times.

Fields of Study & Subjects

graph theory and CDMA systems

Publication details

Journal / source
SIAM Journal on Discrete Mathematics
Volume
40
Issue
2
Pages
675–679
Publication date
7 May 2026
Language
EN