Subsequence Sums
Yahya Ould Hamidoune · Combinatorics Probability Computing · 2003
Let $G$ be a cyclic group of order $n$ and let $\mu = \{x_1,x_2, \dots, x_m\}$ be a sequence of elements of $G$ . Let $k$ be the number of distinct values taken by the sequence $\mu$ . Let $n\wedge \mu$ be the set of the $n$ -subsequence sums. We show that one of the following conditions holds: $\mu$ has a value repeated $n-k+3$ times $n\wedge \mu$ contains a non-null subgroup $|n\wedge \mu|\geq m-n+k-2.$ We conjecture that the last condition could be improved to $|n\wedge \mu|\geq m-n+k-1$ . This conjecture generalizes several known results. We also obtain a generalization of a recent result due to Bollobás and Leader.