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{\bf Aaron D. Jaggard}
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{\bf Subsequence Containment by Involutions}
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Inspired by work of McKay, Morse, and Wilf, we give an exact count
of the involutions in ${\cal S}_{n}$ which contain a given permutation
$\tau\in{\cal S}_{k}$ as a subsequence; this number depends on the
patterns of the first $j$ values of $\tau$ for $1\leq j\leq k$. We
then use this to define a partition of ${\cal S}_{k}$, analogous to
Wilf-classes in the study of pattern avoidance, and examine
properties of this equivalence.  In the process, we show that a
permutation $\tau_1\ldots\tau_k$ is layered iff, for $1\leq j\leq
k$, the pattern of $\tau_1\ldots\tau_j$ is an involution.  We also
obtain a result of Sagan and Stanley counting the standard Young
tableaux of size $n$ which contain a fixed tableau of size $k$ as
a subtableau.

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