Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
A Hopf algebra of subword complexes (Extended abstract)
Nantel Bergeron  1  , Cesar Ceballos  2  
1 : Department of Mathematics and Statistics [Canada]  -  Website
Faculty of Pure and Applied Sciences 4700 Keele Street North York, Ontario, Canada, M3J 1P3 -  Canada
2 : Faculty of Mathematics [Vienna]  -  Website
Oskar-Morgenstern-Platz 1, 1090 Wien -  Autriche

We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acyclic orientations of certain graphs, and show that this Hopf algebra induces a natural non-trivial sub-Hopf algebra on c-clusters in the theory of cluster algebras.

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