Formation width conjecture for abc(acb)tabcabc(acb)^t abc

Let tt be a nonnegative integer, and let fw(u)\mathit{fw}(u) denote the formation width of a sequence uu. Formation width conjecture.

fw(abc(acb)tabc)=2t+3.\mathit{fw}(abc(acb)^{t}abc)=2t+3.

The paper states that this would imply nearly tight bounds on the extremal function Ex(abc(acb)tabc,n)\mathit{Ex}(abc(acb)^{t}abc,n). The conjecture extends the proved result fw(abc(acb)t)=2t+1\mathit{fw}(abc(acb)^t)=2t+1 for t0t\geq 0; its resolution is not given here.

Sources & referencesView supporting material

Primary source

J. T. Geneson, Rohil Prasad and Jonathan Tidor, “Bounding sequence extremal functions with formations”, arXiv:1308.3810 (2014).

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