A pair of dual Hopf algebras on permutations. (English) Zbl 1484.16039
Summary: Hopf algebras are important objects in algebraic combinatorics since they have strong stability. In particular, its dual space is an important tool to study the properties of the original Hopf algebra. Based on the classical shuffle Hopf algebra structure, we have proved that the shuffle product and deconcatenation coproduct on the standard factorizations of permutations define a graded shuffle Hopf algebra on permutations. In this paper, we figure out a new product and a new coproduct on permutations to get the duality of this graded shuffle Hopf algebra.
MSC:
| 16T05 | Hopf algebras and their applications |
| 05A05 | Permutations, words, matrices |
| 08C20 | Natural dualities for classes of algebras |
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