Hopf algebras of \(m\)-permutations, \((m + 1)\)-ary trees, and \(m\)-parking functions

DOI10.1016/j.aam.2020.102019zbMath1436.16047arXiv1403.5962OpenAlexW3009275127MaRDI QIDQ2307437

Jean-Christophe Novelli, Jean-Yves Thibon

Publication date: 27 March 2020

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.5962

zbMATH Keywords

operadsnoncommutative symmetric functionsquasi-symmetric functionsparking functionscombinatorial Hopf algebras

Mathematics Subject Classification ID

Trees (05C05) Symmetric functions and generalizations (05E05) Connections of Hopf algebras with combinatorics (16T30)

Related Items (6)

Three Fuss-Catalan posets in interaction and their associative algebras ⋮ Noncommutative symmetric functions and Lagrange inversion. II: Noncrossing partitions and the Farahat-Higman algebra ⋮ On some quadratic algebras. I \(\frac{1}{2}\): Combinatorics of Dunkl and Gaudin elements, Schubert, Grothendieck, Fuss-Catalan, universal Tutte and reduced polynomials ⋮ A noncommutative cycle index and new bases of quasi-symmetric functions and noncommutative symmetric functions ⋮ Lattices from graph associahedra and subalgebras of the Malvenuto-Reutenauer algebra ⋮ Hopf algebras of parking functions and decorated planar trees

Uses Software

• OEIS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The algebra of binary search trees
• Generalized Stirling permutations, families of increasing trees and urn models
• Noncommutative symmetric functions. VII: Free quasi-symmetric functions revisited
• Free and cofree Hopf algebras.
• A plactic algebra for semisimple Lie algebras
• Duplicial algebras, parking functions, and Lagrange inversion
• Construction of dendriform trialgebras.
• Trees, functional equations, and combinatorial Hopf algebras
• Some remarks on Catalan families
• Chain enumeration and non-crossing partitions
• Hopf algebra of the planar binary trees
• Noncommutative symmetric functions. IV: Quantum linear groups and Hecke algebras at \(q=0\)
• On orbital variety closures in \(\mathfrak{sl}_n\). I: Induced Duflo order.
• Hecke algebras, difference operators, and quasi-symmetric functions
• Noncommutative symmetric functions
• Crystal graphs and \(q\)-analogues of weight multiplicities for the root system \(A_ n\)
• Duality between quasi-symmetric functions and the Solomon descent algebra
• On the hypoplactic monoid
• Polynomial realizations of some combinatorial Hopf algebras
• Noncommutative symmetric functions and Lagrange inversion
• The generalized Schröder theory
• Hopf algebras and dendriform structures arising from parking functions
• NONCOMMUTATIVE SYMMETRIC FUNCTIONS VI: FREE QUASI-SYMMETRIC FUNCTIONS AND RELATED ALGEBRAS
• Counting smaller trees in the Tamari order

This page was built for publication: Hopf algebras of \(m\)-permutations, \((m + 1)\)-ary trees, and \(m\)-parking functions