Counting Words with Laguerre Series
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...
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| Published in | The Electronic journal of combinatorics Vol. 21; no. 2 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.04.2014
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| Online Access | Get full text |
| ISSN | 1077-8926 1097-1440 1077-8926 |
| DOI | 10.37236/3500 |
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| Summary: | 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. |
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| ISSN: | 1077-8926 1097-1440 1077-8926 |
| DOI: | 10.37236/3500 |