Chatel, G. and Pilaud, V. - The Cambrian Hopf Algebra

dmtcs:2533 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
The Cambrian Hopf Algebra

Authors: Chatel, G. and Pilaud, V.

Cambrian trees are oriented and labeled trees which fulfill local conditions around each node generalizing the conditions for classical binary search trees. Based on the bijective correspondence between signed permutations and leveled Cambrian trees, we define the Cambrian Hopf algebra generalizing 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. Finally, we define multiplicative bases of the Cambrian algebra and study structural and combinatorial properties of their indecomposable elements.


Source : oai:HAL:hal-01337839v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: Combinatorial Hopf algebras,Cambrian lattices,Cambrian trees,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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