Geodesic
Counting words with Laguerre series
Jair Taylor1
1University of Washington
The electronic journal of combinatorics, Tome 21 (2014) no. 2
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We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of weighted sums of Laguerre polynomials with parameter $\alpha = -1$. We describe how such a series can be computed by finding an appropriate ordinary generating function and applying a certain transformation. We use this technique to find the generating function for the number of $k$-ary words avoiding any vincular pattern that has only ones, as well as words cyclically avoiding vincular patterns with only ones whose runs of ones between dashes are all of equal length.
DOI : 10.37236/3500
Classification : 05A05, 05A15, 42C05, 68R15
Mots-clés : Laguerre polynomial, orthogonal polynomial, combinatorics on words, vincular pattern

Jair Taylor  1

1 University of Washington 
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     author = {Jair Taylor},
     title = {Counting words with {Laguerre} series},
     journal = {The electronic journal of combinatorics},
     year = {2014},
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     number = {2},
     doi = {10.37236/3500},
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Jair Taylor. Counting words with Laguerre series. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/3500

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