Noncommutative symmetric functions and Lagrange inversion

  title={Noncommutative symmetric functions and Lagrange inversion},
  author={Jean-Christophe Novelli and Jean-Yves Thibon},
  journal={Adv. Appl. Math.},
We compute the non-commutative Frobenius characteristic of the natural action of the 0-Hecke algebra on parking functions, and obtain as corollaries various forms of the non-commutative Lagrange inversion formula. 
Noncommutative Bessel symmetric functions
The consideration of tensor products of 0-Hecke algebra modules leads to natural analogs of the Bessel J-functions in the algebra of noncommutative symmetric functions. This provides a simpleExpand
Noncommutative Symmetric Bessel Functions
Abstract The consideration of tensor products of 0-Hecke algebramodules leads to natural analogs of the Bessel $J$ -functions in the algebra of noncommutative symmetric functions. This provides aExpand
We give a new combinatorial interpretation of the noncommutative Lagrange inversion formula, more precisely, of the formula of Brouder-FrabettiKrattenthaler for the antipode of the noncommutative FaàExpand
Noncommutative Symmetric Functions and Lagrange Inversion II: Noncrossing partititions and the Farahat-Higman algebra
We introduce a new pair of mutually dual bases of noncommutative symmetric functions and quasi-symmetric functions, and use it to derive generalizations of several results on the reduced incidenceExpand
Combinatorial properties of the noncommutative Faà di Bruno algebra
We give a new combinatorial interpretation of the noncommutative Lagrange inversion formula, more precisely, of the formula of Brouder–Frabetti–Krattenthaler for the antipode of the noncommutativeExpand
A One-parameter Deformation of the Noncommutative Lagrange Inversion Formula
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Noncommutative symmetric functions and combinatorial Hopf algebras
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One of the main virtues of trees is the representation of formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differentialExpand
Non-commutative Frobenius characteristic of generalized parking functions -- Application to enumeration
We give a recursive definition of generalized parking function that allows us to view them as a species. From there we compute a non-commutative characteristic of the generalized parking functionExpand
Lagrange inversion
  • I. Gessel
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 2016
We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.


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The Lagrange inversion formula is generalized to formal power series in noncommutative variables. A g-analog is obtained by applying a linear operator to the noncommutative formula beforeExpand
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We present representation theoretical interpretations ofquasi-symmetric functions and noncommutative symmetric functions in terms ofquantum linear groups and Hecke algebras at q = 0. We obtain inthisExpand
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Noncommutative Symmetric Functions Vi: Free Quasi-Symmetric Functions and Related Algebras
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Symmetric functions Symmetric functions as operators and $\lambda$-rings Euclidean division Reciprocal differences and continued fractions Division, encore Pade approximants Symmetrizing operatorsExpand
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Noncommutative Symmetric Functions II: Transformations of Alphabets
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Commutative Hopf algebras of permutations and trees
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A Hopf algebra of parking functions
If the moments of a probability measure on $\R$ are interpreted as a specialization of complete homogeneous symmetric functions, its free cumulants are, up to sign, the corresponding specializationsExpand
Noncommutative symmetric functions
This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in anExpand