Diagonal Temperley-Lieb invariants and harmonics.

Aval, J.-C.; Bergeron, F.; Bergeron, N.

Displaying similar documents to “Diagonal Temperley-Lieb invariants and harmonics.”

Hopf algebras of words and overlapping shuffle algebra (Retracted)

Olivera Marković (2007)

Kragujevac Journal of Mathematics

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Grothendieck bialgebras, partition lattices, and symmetric functions in noncommutative variables.

Bergeron, N., Hohlweg, C., Rosas, M., Zabrocki, M. (2006)

The Electronic Journal of Combinatorics [electronic only]

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Canonical characters on simple graphs

Tanja Stojadinović (2013)

Czechoslovak Mathematical Journal

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A multiplicative functional on a graded connected Hopf algebra is called the character. Every character decomposes uniquely as a product of an even character and an odd character. We apply the character theory of combinatorial Hopf algebras to the Hopf algebra of simple graphs. We derive explicit formulas for the canonical characters on simple graphs in terms of coefficients of the chromatic symmetric function of a graph and of canonical characters on quasi-symmetric functions. These...

Invariant and coinvariant spaces for the algebra of symmetric polynomials in non-commuting variables.

Bergeron, François, Lauve, Aaron (2010)

The Electronic Journal of Combinatorics [electronic only]

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Colored trees and noncommutative symmetric functions.

Szczesny, Matt (2010)

The Electronic Journal of Combinatorics [electronic only]

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Some new methods in the theory of $m$ -quasi-invariants.

Bell, J., Garsia, A.M., Wallach, N. (2005)

The Electronic Journal of Combinatorics [electronic only]

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Tensorial square of the hyperoctahedral group coinvariant space.

Bergeron, François, Biagioli, Riccardo (2006)

The Electronic Journal of Combinatorics [electronic only]

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Symmetrization of brace algebra

Daily, Marilyn, Lada, Tom

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Summary: We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra. We also show that the symmetrization of the natural brace structure on $⨁_{k \geq 1} Hom (V^{\otimes k}, V)$ coincides with the natural symmetric brace structure on $⨁_{k \geq 1} Hom {(V^{\otimes k}, V)}^{a s}$ , the direct sum of spaces of antisymmetric maps $V^{\otimes k} \to V$ .

Hopf algebras and dendriform structures arising from parking functions

Jean-Christophe Novelli, Jean-Yves Thibon (2007)

Fundamenta Mathematicae

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We introduce a graded Hopf algebra based on the set of parking functions (hence of dimension ${(n + 1)}^{n - 1}$ in degree n). This algebra can be embedded into a noncommutative polynomial algebra in infinitely many variables. We determine its structure, and show that it admits natural quotients and subalgebras whose graded components have dimensions respectively given by the Schröder numbers (plane trees), the Catalan numbers, and powers of 3. These smaller algebras are always bialgebras and belong to...