Set Theory and Logic


A Note on the Length of Maximal Arithmetic Progressions in Random Subsets

Authors: Yilun Shang

Let $U^{(n)}$ denote the maximal length arithmetic progression in a non-uniform random subset of $\{0,1\}^n$, where $1$ appears with probability $p_n$. By using dependency graph and Stein-Chen method, we show that $U^{(n)}-c_n\ln n$ converges in law to an extreme type distribution with $\ln p_n=-2/c_n$. Similar result holds for $W^{(n)}$, the maximal length aperiodic arithmetic progression (mod $n$).

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[v1] 2014-10-04 20:57:05

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