Counting words with Laguerre polynomials
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 g...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2013-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2369/pdf |
| _version_ | 1797270273522663424 |
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| author | Jair Taylor |
| author_facet | Jair Taylor |
| author_sort | Jair Taylor |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:01:39Z |
| format | Article |
| id | doaj.art-443cad29d0a74ea09a3d75e51996a65c |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:01:39Z |
| publishDate | 2013-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-443cad29d0a74ea09a3d75e51996a65c2024-03-07T14:52:36ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502013-01-01DMTCS Proceedings vol. AS,...Proceedings10.46298/dmtcs.23692369Counting words with Laguerre polynomialsJair Taylor0Department of Mathematics [Seattle]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.https://dmtcs.episciences.org/2369/pdflaguerre polynomialorthogonal polynomialcombinatorics on wordsvincular pattern[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Jair Taylor Counting words with Laguerre polynomials Discrete Mathematics & Theoretical Computer Science laguerre polynomial orthogonal polynomial combinatorics on words vincular pattern [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Counting words with Laguerre polynomials |
| title_full | Counting words with Laguerre polynomials |
| title_fullStr | Counting words with Laguerre polynomials |
| title_full_unstemmed | Counting words with Laguerre polynomials |
| title_short | Counting words with Laguerre polynomials |
| title_sort | counting words with laguerre polynomials |
| topic | laguerre polynomial orthogonal polynomial combinatorics on words vincular pattern [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2369/pdf |
| work_keys_str_mv | AT jairtaylor countingwordswithlaguerrepolynomials |