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{\bf Mark Lipson}
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{\bf Completion of the Wilf-Classification of 3-5 Pairs Using Generating Trees}
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A permutation $\pi$ is said to avoid the permutation $\tau$ if no
subsequence in $\pi$ has the same order relations as $\tau$. Two sets
of permutations $\Pi_1$ and $\Pi_2$ are Wilf-equivalent if, for all
$n$, the number of permutations of length $n$ avoiding all of the
permutations in $\Pi_1$ equals the number of permutations of length
$n$ avoiding all of the permutations in $\Pi_2$. Using generating
trees, we complete the problem of finding all Wilf-equivalences among
pairs of permutations of which one has length 3 and the other has
length 5 by proving that $\{123,32541\}$ is Wilf-equivalent to
$\{123,43251\}$ and that $\{123,42513\}$ is Wilf-equivalent to $\{132,
34215\}$. In addition, we provide generating trees for fourteen other
pairs, among which there are two examples of pairs that give rise to
isomorphic generating trees.
\bye