Geodesic
Counting words by number of occurrences of some patterns
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/630
Classification : 05A05, 68R15
Mots-clés : classical pattern, occurrence, asymptotics, word, partially ordered pattern 
@article{10_37236_630,
     author = {Zhicheng Gao and Andrew MacFie and Daniel Panario},
     title = {Counting words by number of occurrences of some patterns},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/630},
     zbl = {1227.05016},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/630/}
}
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Zhicheng Gao; Andrew MacFie; Daniel Panario. Counting words by number of occurrences of some patterns. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/630

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