Yilun Shang. A note on the length of maximal arithmetic progressions in random subsets


Natural Sciences / Mathematics / Calculus / Analysis

Submitted on: Nov 16, 2012, 14:19:17

Description: 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 $U^{(n)}-c_nln n$ 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 $n$).

The abstract of this article will be published in the November 2012 issue of "Intellectual Archive Bulletin", ISSN 1929-1329.

The Library and Archives Canada reference page: collectionscanada.gc.ca/ourl/res.php?url_ver=Z39.88......

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a note on the length of maximal arithmetic progressions in random subsets.pdf



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