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Discrete Mathematics & Theoretical Computer Science |
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.
Source : ScholeXplorer
IsRelatedTo ARXIV 0808.3926 Source : ScholeXplorer IsRelatedTo DOI 10.1088/1751-8113/41/42/425207 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.0808.3926
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