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Structure of the Malvenuto-Reutenauer Hopf Algebra of Permutations (Extended Abstract)
Hopf algebra and algebra algebraic function
2014/12/29
We analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determine its primitive el...
Combinatorial Hopf Algebra and Generalized Dehn-Sommerville Relations
Combination of hopf algebra hopf algebra linear function generating function combination
2014/12/29
A combinatorial Hopf algebra is a graded connected Hopf algebra over a field k equipped with a character (multiplicative linear functional) : H → k. We show that the terminal object in the category ...