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A+ CATEGORY SCIENTIFIC UNIT

On additive bases II

Volume 168 / 2015

Weidong Gao, Dongchun Han, Guoyou Qian, Yongke Qu, Hanbin Zhang Acta Arithmetica 168 (2015), 247-267 MSC: 11P70, 11B50, 11B75. DOI: 10.4064/aa168-3-3

Abstract

Let 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 \subseteq G, S contains at most |H|-1 terms from H. Let \mathsf c_0(G) be the smallest integer t such that every regular sequence S over G of length |S|\geq 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 \mathsf c_0(G) has been determined previously only for the elementary abelian groups. In this paper, we determine \mathsf c_0(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\oplus C_{p^n} with n\geq 2.

Authors

  • Weidong GaoCenter for Combinatorics
    Nankai University
    Tianjin 300071, P.R. China
    e-mail
  • Dongchun HanCenter for Combinatorics
    Nankai University
    Tianjin 300071, P.R. China
    e-mail
  • Guoyou QianMathematical College
    Sichuan University
    Chengdu 610064, P.R. China
    e-mail
  • Yongke QuDepartment of Mathematics
    Luoyang Normal University
    Luoyang 471022, P.R. China
    e-mail
  • Hanbin ZhangCenter for Combinatorics
    Nankai University
    Tianjin 300071, P.R. China
    e-mail

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