## Bollobas-Leader Conjecture

Matt has proposed another problem from additive number theory for the next Problem of
the month.

**Bollobas-Leader Conjecture ([1]):**
Let a_{1}, a_{2}, ..., a_{n-1+r} be a sequence of elements from
the group **Z**_{n}^{2} such that every nonempty subsequence
of these elements has non-zero sum. Then the number of distinct elements
representable as a subsequence sum is minimized when a_{1}, a_{2},
...,
a_{n-1+r} consists of n - 1 copies of (1,0) and r copies of (0,1).

Bibliography:

[1] B. Bollobas, I. Leader, The number of k-sums modulo k, J. Number Theory
78 (1999) 27-35.

Send comments to Bojan.Mohar@uni-lj.si

##### Revised: avgust 05, 2006.