Résumé : The associative symmetric operad $As$ is the linear span of all permutations endowed with an operation allowing us to insert a permutation into another one. This structure is rich both under a combinatorial and an algebraic point of view. In this context, Aguiar and Livernet have constructed alternative bases of $As$ relating it with the combinatorics of the weak order on permutations. In this talk, I will present a family of analogous operads, defined on some families of words of integers. These operads are substructures of a master structure called interstice operad. We obtain in this way operads on objects in correspondence with permutations, increasing trees, Fuss-Catalan objects, or walks in rectangles. One of the peculiarities of some of these operads is that, despite to their relative simplicity, some are infinitely generated and have nonquadratic and nonhomogeneous nontrivial relations. Joint work with Camille Combe.

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Dernière modification : Thursday 21 November 2024

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