Emergent Mind
Stanley-Wilf limits are typically exponential
(1310.8378)
Published Oct 31, 2013
in
math.CO
and
cs.DM
Abstract
For a permutation $\pi$, let $S{n}(\pi)$ be the number of permutations on $n$ letters avoiding $\pi$. Marcus and Tardos proved the celebrated Stanley-Wilf conjecture that $L(\pi)= \lim{n \to \infty} S_n(\pi){1/n}$ exists and is finite. Backed by numerical evidence, it has been conjectured by many researchers over the years that $L(\pi)=\Theta(k2)$ for every permutation $\pi$ on $k$ letters. We disprove this conjecture, showing that $L(\pi)=2{k{\Theta(1)}}$ for almost all permutations $\pi$ on $k$ letters.
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