Enumeration of zero-sum subsequences: A proof of Bialostocki-Lotspeich conjecture

Let Cₙ be a cyclic group of order n≥ 2, and let S=g₁·…· g_ be a sequence over Cₙ, with repetitions allowed. We denote by N₀ⁿ(S) the number of subsets I⊆[1,] with $|I|=n$ and ∑i∈ Igᵢ=0. A conjecture proposed by Bialostocki and Lotspeich in 1992 states that N₀ⁿ(S)≥ |S|/2n+ |S|/2n. Several partial results toward this conjecture are known. In this paper, we prove this conjecture completely.