Hopf algebras on planar trees and permutations
Keyword(s):
We endow the space of rooted planar trees with the structure of a Hopf algebra. We prove that variations of such a structure lead to Hopf algebras on the spaces of labeled trees, [Formula: see text]-trees, increasing planar trees and sorted trees. These structures are used to construct Hopf algebras on different types of permutations. In particular, we obtain new characterizations of the Hopf algebras of Malvenuto–Reutenauer and Loday–Ronco via planar rooted trees.
2008 ◽
Vol 2
(1)
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pp. 147-167
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Keyword(s):
Keyword(s):
2018 ◽
Vol 2020
(21)
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pp. 7558-7616
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Keyword(s):
1993 ◽
Vol 08
(25)
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pp. 4521-4545
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1967 ◽
Vol 19
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pp. 350-360
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