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Plane posets, special posets, and permut...

Foissy, Loïc...

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Plane posets, special posets, and permutations by Foissy, Loïc ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	11-08-2023
Summary	We study the self-dual Hopf algebra $\h\_{\SP}$ of special posets introduced by Malvenuto and Reutenauer and the Hopf algebra morphism from $\h\_{\SP}$ to to the Hopf algebra of free quasi-symmetric functions $\FQSym$ given by linear extensions. In particular, we construct two Hopf subalgebras both isomorphic to $\FQSym$; 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 transformations on special posets. The restriction of the Hopf pairing of $\h\_{\SP}$ 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.An error in Section 7 has been noticed by Darij Grinberg, and the text has been modified accordingly.
ISBN	-
Item Type	Article
File Type	pdf
File Size	30.00 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1109.1101

Citation

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AMA 11th EditionReferences

Foissy, Loïc. Plane posets, special posets, and permutations. Australian National University. August 11, 2023. Accessed October 01, 2025. https://online.provdatabase.com/cite/15713

APA 7th EditionReferences

Foissy, Loïc. (2023). Plane posets, special posets, and permutations. Australian National University. https://online.provdatabase.com/cite/15713

Chicago 17th EditionReferences

Foissy, Loïc. Plane posets, special posets, and permutations. Australian National University. 2023. https://online.provdatabase.com/cite/15713

HarvardReferences

Foissy, Loïc. (2023). Plane posets, special posets, and permutations. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/15713. (Accessed 01 October 2025).

Harvard AustraliaReferences

Foissy, Loïc, 2023, Plane posets, special posets, and permutations, Australian National University, viewed 01 October 2025, <https://online.provdatabase.com/cite/15713>

MLA 9th EditionWorks Cited

Foissy, Loïc. Plane posets, special posets, and permutations. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/15713.

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