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When does a pattern-avoiding permutation avoid additional patterns?

Mathematical Physics & Probability

Speaker: Sam Miner, Pomona College
Location: 1147 MSB
Start time: Wed, Mar 15 2017, 4:10PM

A permutation of length n contains a pattern of length k if one can find k elements within the original permutation which are in the same relative order as the elements of the pattern. If a permutation does not contain the pattern, we say it avoids the pattern. The study of pattern-avoiding permutations began in earnest with Knuth in the 1960's, and has seen much interest in recent years. For example, one can ask questions of enumerating classes, of what the typical permutation in such a pattern-avoiding class looks like, and more.

In this talk, we will discuss when a pattern-avoiding permutation is likely to avoid additional patterns as well. Specifically, we will show instances of classes which, as the length of the permutation gets large, have probability tending to 1 of avoiding additional patterns.