Bollobas-Leader Conjecture

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

Bollobas-Leader Conjecture ([1]): Let a1, a2, ..., an-1+r be a sequence of elements from the group Zn2 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 a1, a2, ..., an-1+r consists of n - 1 copies of (1,0) and r copies of (0,1).


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

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Revised: avgust 05, 2006.