On additive bases II

• Autorzy: Weidong Gao , Dongchun Han , Guoyou Qian , Yongke Qu , Hanbin Zhang
• Języki publikacji: EN

Abstrakty

EN

Let G be an additive finite abelian group, and let S be a sequence over G. We say that S is regular if for every proper subgroup H ⊆ G, S contains at most |H|-1 terms from H. Let 𝖼₀(G) be the smallest integer t such that every regular sequence S over G of length |S| ≥ t forms an additive basis of G, i.e., every element of G can be expressed as the sum over a nonempty subsequence of S. The constant 𝖼₀(G) has been determined previously only for the elementary abelian groups. In this paper, we determine 𝖼₀(G) for some groups including the cyclic groups, the groups of even order, the groups of rank at least five, and all the p-groups except $G=C_p ⊕ C_{p^n}$ with n≥ 2.

Kategorie tematyczne

• 11B75: Other combinatorial number theory
• 11P70: Inverse problems of additive number theory, including sumsets
• 11B50: Sequences (mod m )

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 168
• Numer: 3
• Strony: 247-267

Daty

wydano

2015

Twórcy

autor

Weidong Gao

• Center for Combinatorics, Nankai University, Tianjin 300071, P.R. China

autor

Dongchun Han

• Center for Combinatorics, Nankai University, Tianjin 300071, P.R. China

autor

Guoyou Qian

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

autor

Yongke Qu

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

autor

Hanbin Zhang

• Center for Combinatorics, Nankai University, Tianjin 300071, P.R. China

Identyfikatory

DOI

10.4064/aa168-3-3