Zero-Sum Flows for Steiner Triple Systems

Given a 2-(v;k; ) design, S = (X;B), a zero-sum n-ow ofS is a map f :B! f 1;:::; (n 1)g such that for any point x2 X, the sum of f around all the blocks incident with x is zero. It has been conjectured that every Steiner triple system, STS(v), on v points (v > 7) admits a zero-sum 3-ow. We show that for every pair ( v; ), for which a triple system, TS(v; ) exists, there exists one which has a zero-sum 3-ow,

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