The Prague Stringology Conference 2006

Frantisek Franek and Qian Yang

An Asymptotic Lower Bound for the Maximal-Number-of-Runs Function

An asymptotic lower bound for the maxrun function r(n) = max {number of runs in string x | all strings x of length n} is presented. More precisely, it is shown that for any ε > 0, (α-ε)n is an asymptotic lower bound, where α = 3/(1+50.5) ≈ 0.927. A recent construction of an increasing sequence of binary strings "rich in runs" is modified and extended to prove the result.

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