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Bialostocki-Lotspeich Conjecture

The Bialostocki-Lotspeich conjecture gives a lower bound for the number of prescribed-length zero-sum subsequences in a cyclic group. Let S=(s_1,...,s_l) be a sequence in a cyclic group of group order n>=2. Let N_0^n(S) count the n-element subsets of indices whose corresponding terms sum to 0. Repeated values occupy distinct positions and are counted accordingly. The conjectured inequality is

N_0^n(S)>=(|_l/2_|; n)+([l/2]; n),

where |_x_| and [x] denote the floor function and ceiling function, and a binomial coefficient is 0 when its upper argument is smaller than n. Wang and Zeng (2026) proved the conjecture, stated in Caro (1996).

For l=2n-1, the right side is 1, recovering the Erdős-Ginzburg-Ziv theorem. Wang and Zeng (2026) report AI assistance with mathematical exploration and checking the arguments.

See also

Zero-Sum Sequence

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References

Caro, Y. "Zero-Sum Problems-A Survey." Disc. Math. 152, 93-113, 1996.Wang, G. and Zeng, X. "Enumeration of Zero-Sum Subsequences: A Proof of Bialostocki-Lotspeich Conjecture." 27 Oct 2026. https://arxiv.org/abs/2610.37125.

Cite this as:

Weisstein, Eric W. "Bialostocki-Lotspeich Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Bialostocki-LotspeichConjecture.html

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