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Article Dans Une Revue Advances in Mathematics Année : 2017

Cambrian Hopf algebras

Résumé

Cambrian trees are oriented and labeled trees which fulfill local conditions around each node generalizing the conditions for classical binary search trees. Based on a natural surjection from signed permutations to Cambrian trees, we define the Cambrian Hopf algebra extending J.-L. Loday and M. Ronco's algebra on binary trees. We describe combinatorially the products and coproducts of both the Cambrian algebra and its dual in terms of operations on Cambrian trees. We then construct the Baxter-Cambrian algebra which extends S. Law and N. Reading's Baxter Hopf algebra on rectangulations and S. Giraudo's equivalent Hopf algebra on twin binary trees.
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hal-02343339 , version 1 (02-11-2019)

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Grégory Chatel, Vincent Pilaud. Cambrian Hopf algebras. Advances in Mathematics, 2017, 311, pp.598-633. ⟨10.1016/j.aim.2017.02.027⟩. ⟨hal-02343339⟩
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