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STRUCTURE OF THE MALVENUTO-REUTENAUER HOPF ALGEBRA OF PERMUTATIONS
Hopf algebra symmetric group weak order quasi-symmetric function
2015/8/14
We analyze the structure of theMalvenuto-Reutenauer Hopf algebraSSym
of permutations in detail. We give explicit formulas for its antipode, prove that it is
a cofree coalgebra, determine its primiti...
COCOMMUTATIVE HOPF ALGEBRAS OF PERMUTATIONS AND TREES
Hopf algebr rooted tree planar binary tree symmetric group
2015/8/14
Consider the coradical filtrations of the Hopf algebras of planar binary
trees of Loday and Ronco and of permutations of Malvenuto and Reutenauer. We
give explicit isomorphisms showing that the asso...
THE HOPF ALGEBRA OF UNIFORM BLOCK PERMUTATIONS
Hopf algebra factorizable inverse monoid uniform block permutation
2015/8/14
We introduce the Hopf algebra of uniform block permutations and show that
it is self-dual, free, and cofree. These results are closely related to the fact that uniform
block permutations form a fact...
Algebraic and combinatorial structures on Baxter permutations
Algebraic combinatorial structures Baxter permutations
2010/11/23
We construct a Hopf subalgebra of the Hopf algebra of Free quasi-symmetric functions whose bases are indexed by objects belonging to the Baxter combinatorial family (i.e. Baxter permutation, pairs of ...