On n-sum in an abelian group

[Math. Dept.]

May 22, 2018  14:50-15:50

W303  School of Mathematics

[colloquium] Weidong Gao20180522-01.png

SPEAKER

Weidong Gao (Center for Combinatorics of Nankai University)

ABSTRACT

Let G be an additive abelian group, and n ≥ 1 be an integer, and let S be a sequence over G of length |S | ≥ n + 1. Let Σn(S ) denote the set consisting of all elements in G which can be expressed as the sum over a subsequence of S of length n. We prove that, either ng ∈ Σn(S ) for some term g ∈ supp(S ) with maximal multiplicity, or |Σn(S )| ≥ min{n+1, |S |−n+| supp(S )|−1}, when G is finite cyclic and n = |G|, which confirms a conjecture raised by Y.O. Hamidoune in 2003, where |supp(S )| denotes the number of distinct terms that occur in S .

SUPPORTED BY

School of Mathematics, Sichuan University

LECTURE NOTES

TMCSC180522a_Weidong Gao_On n-sums in an abelian group

VIDEO

  • On n-sum in an abelian group
  • 14:50 - 15:50, 2018-05-22 at W303 School of Mathematics
  • Weidong Gao (Center for Combinatorics of Nankai University)