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Counting words with Laguerre polynomials

Abstract : We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of formal sums of Laguerre polynomials. We use this method to find the generating function for $k$-ary words avoiding any vincular pattern that has only ones. We also give generating functions for $k$-ary words cyclically avoiding vincular patterns with only ones whose runs of ones between dashes are all of equal length, as well as the analogous results for compositions.
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https://hal.inria.fr/hal-01229684
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Submitted on : Tuesday, November 17, 2015 - 10:19:54 AM
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Long-term archiving on: : Thursday, February 18, 2016 - 11:37:54 AM

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Jair Taylor. Counting words with Laguerre polynomials. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.1101-1112, ⟨10.46298/dmtcs.2369⟩. ⟨hal-01229684⟩

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