Plane posets, special posets, and permutations

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• 作者：L. Foissy ^{loic.foissy@univ-reims.fr}
• 关键词：06A11 ; 05A05 ; 16W30 ; 17A30
• 刊名：Advances in Mathematics
• 出版年：2013
• 出版时间：20 June, 2013
• 年：2013
• 卷：240
• 期：Complete
• 页码：24-60
• 全文大小：374 K

文摘

We study the self-dual Hopf algebra of special posets introduced by Malvenuto and Reutenauer and the Hopf algebra morphism from to the Hopf algebra of free quasi-symmetric functions given by linear extensions. In particular, we construct two Hopf subalgebras both isomorphic to ; the first one is based on plane posets, the second one on heap-ordered forests. An explicit isomorphism between these two Hopf subalgebras is also defined, with the help of two combinatorial transformations on special posets. The restriction of the Hopf pairing of to these Hopf subalgebras and others is also studied, as well as certain isometries between them. These problems are solved using duplicial and dendriform structures.