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{\bf Narad Rampersad}
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{\bf Further Applications of a Power Series Method for Pattern Avoidance}
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In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is
said to avoid a pattern $p$ over an alphabet $\Delta$ if there is no
factor $x$ of $w$ and no non-erasing morphism $h$ from $\Delta^*$ to
$\Sigma^*$ such that $h(p) = x$. Bell and Goh have recently applied
an algebraic technique due to Golod to show that for a certain wide
class of patterns $p$ there are exponentially many words of length $n$
over a $4$-letter alphabet that avoid $p$. We consider some further
consequences of their work. In particular, we show that any pattern
with $k$ variables of length at least $4^k$ is avoidable on the binary
alphabet. This improves an earlier bound due to Cassaigne and Roth.
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