A characterization of sequences with the minimum number of k-sums modulo k

• Autorzy: Xingwu Xia , Yongke Qu , Guoyou Qian
• Języki publikacji: EN

Abstrakty

EN

Let G be an additive abelian group of order k, and S be a sequence over G of length k+r, where 1 ≤ r ≤ k-1. We call the sum of k terms of S a k-sum. We show that if 0 is not a k-sum, then the number of k-sums is at least r+2 except for S containing only two distinct elements, in which case the number of k-sums equals r+1. This result improves the Bollobás-Leader theorem, which states that there are at least r+1 k-sums if 0 is not a k-sum.

Kategorie tematyczne

• 11B30: Arithmetic combinatorics; higher degree uniformity
• 11B50: Sequences (mod m )

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 136
• Numer: 1
• Strony: 51-56

Daty

wydano

2014

Twórcy

autor

Xingwu Xia

• Department of Mathematics, Luoyang Normal University, LuoYang 471022, P.R. China

autor

Yongke Qu

• Department of Mathematics, Luoyang Normal University, LuoYang 471022, P.R. China

autor

Guoyou Qian

• Mathematical College, Sichuan University, Chengdu 610064, P.R. China

Identyfikatory

DOI

10.4064/cm136-1-5