Signaletic operads
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866929352378155008 |
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| author | Hivert, Florent Pilaud, Vincent |
| author_facet | Hivert, Florent Pilaud, Vincent |
| contents | We introduce $k$-signaletic operads and their Koszul duals, generalizing the dendriform, diassociative and duplicial operads (which correspond to the $k=1$ case). We show that the Koszul duals of the $k$-signaletic operads act on multipermutations and that the resulting algebras are free, thus providing combinatorial models for these operads. Finally, motivated by these actions on multipermutations, we introduce similar operations on multiposets which yield yet another relevant operad obtained as Manin powers of the $L$-operad. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_02228 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Signaletic operads Hivert, Florent Pilaud, Vincent Combinatorics 18D50, 16T30, 05E15, 05C05, 68Q42 We introduce $k$-signaletic operads and their Koszul duals, generalizing the dendriform, diassociative and duplicial operads (which correspond to the $k=1$ case). We show that the Koszul duals of the $k$-signaletic operads act on multipermutations and that the resulting algebras are free, thus providing combinatorial models for these operads. Finally, motivated by these actions on multipermutations, we introduce similar operations on multiposets which yield yet another relevant operad obtained as Manin powers of the $L$-operad. |
| title | Signaletic operads |
| topic | Combinatorics 18D50, 16T30, 05E15, 05C05, 68Q42 |
| url | https://arxiv.org/abs/1906.02228 |