Polynomial realizations of some combinatorial Hopf algebras

DOI10.4171/JNCG/151zbMath1290.05153arXiv1009.2067MaRDI QIDQ2450777

Jean-Christophe Novelli, Jean-Yves Thibon, Loïc Foissy

Publication date: 16 May 2014

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.2067

zbMATH Keywords

parking functionsfree quasi-symmetric functionsHopf algebras of decorated rooted trees

Mathematics Subject Classification ID

Trees (05C05) Symmetric functions and generalizations (05E05) Hopf algebras and their applications (16T05) Associative rings and algebras with additional structure (16W99)

Related Items

The Hopf algebra of finite topologies and mould composition, Hopf algebras of \(m\)-permutations, \((m + 1)\)-ary trees, and \(m\)-parking functions, Realizations of Hopf algebras of graphs by alphabets

Cites Work

• Unnamed Item
• The algebra of binary search trees
• The Hopf algebras of decorated rooted trees. II
• Non-commutative Hopf algebra of formal diffeomorphisms.
• Bidendriform bialgebras, trees, and free quasi-symmetric functions.
• Commutative combinatorial Hopf algebras.
• Hopf-algebraic structure of combinatorial objects and differential operators
• Hopf algebras, renormalization and noncommutative geometry
• The Hopf algebras of decorated rooted trees. I
• Noncommutative symmetric functions
• An analogue of the plactic monoid for binary search trees
• Ordered Forests and Parking Functions
• Hopf Algebras of Heap Ordered Trees and Permutations
• NONCOMMUTATIVE SYMMETRIC FUNCTIONS VI: FREE QUASI-SYMMETRIC FUNCTIONS AND RELATED ALGEBRAS
• Ordered Forests, Permutations, and Iterated Integrals
• Geometric Numerical Integration
• COMBINATORIAL HOPF ALGEBRAS IN QUANTUM FIELD THEORY I