An asymptotic Lower Bound for the Maximal Number of Runs in a String
نویسندگان
چکیده
An asymptotic lower bound for the maxrun function ρ(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+ √ 5 ≈ 0.927. A recent construction of an increasing sequence of binary strings “rich in runs” is modified and extended to prove the result.
منابع مشابه
An asymptotic lower bound for the maximal-number-of-runs function
An asymptotic lower bound for the maxrun function ρ(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+ √ 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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ورودعنوان ژورنال:
- Int. J. Found. Comput. Sci.
دوره 19 شماره
صفحات -
تاریخ انتشار 2008