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{\bf Zhicheng Gao, Andrew MacFie and Daniel Panario}
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{\bf Counting Words by Number of Occurrences of Some Patterns}
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We give asymptotic expressions for the number of words containing a given
number of occurrences of a pattern for two families of patterns with two
parameters each. One is the family of classical patterns in the form
$22\cdots 212 \cdots 22$ and the other is a family of partially ordered
patterns. The asymptotic expressions are in terms of the number of solutions
to an equation, and for one subfamily this quantity is the number of integer
partitions into $q$th order binomial coefficients.
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