Asymptotics for dependent sums of random vectors

We consider sequences of length m of n‐tuples each with k nonzero entries chosen randomly from an Abelian group or finite field. For what values of m does there exist a subsequence which is zero‐sum or linearly dependent, respectively? We report some results relating to these problems. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 267–292, 1999