The conjecture that the maximum Frobenius discrepancy for three generators is 14

Let gi(X)g_i(X) denote the relevant Frobenius-number discrepancy quantity for a set XX of generators, and let f(3)f(3) be the corresponding maximum discrepancy over sets of cardinality three. The example

g14(8,9,15)=172,g_{14}(8,9,15)=172, g15(8,9,15)=169g_{15}(8,9,15)=169

shows that f(3)14f(3)\leq 14.

Frobenius discrepancy conjecture for three generators.

f(3)=14.f(3)=14.

The paper states that the value of f(3)f(3) is not known; the displayed example supplies only the upper bound, so the equality remains open.

Sources & referencesView supporting material

Primary source

Jeffrey Shallit and James Stankewicz, “Unbounded discrepancy in Frobenius numbers”, arXiv:1003.0021 (2010).

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