Results 11 to 20 of about 7,293 (133)

Combinatorial Hopf algebras from renormalization [PDF]

Journal of Algebraic Combinatorics, 2009
In this paper we describe the right-sided combinatorial Hopf structure of three Hopf algebras appearing in the context of renormalization in quantum field theory: the non-commutative version of the Fa\`a di Bruno Hopf algebra, the non-commutative version
Alessandra Frabetti, Ch. Brouder, Ch. Brouder, Ch. Brouder, Ch. Brouder, Christian Brouder, D. Guin, D. Kreimer, F. Chapoton, Frédéric Menous, J.-L. Loday, J.-L. Loday, J.-L. Loday, L. Foissy, M. Ronco, R. Grossman   +15 more
core   +14 more sources

Combinatorial Hopf algebras and generalized Dehn-Sommerville relations [PDF]

Compositio Mathematica, 2003
A combinatorial Hopf algebra is a graded connected Hopf algebra over a field $F$ equipped with a character (multiplicative linear functional) $\zeta:H\to F$.
Aguiar, Marcelo, Bergeron, Nantel, Sottile, Frank   +2 more
core   +7 more sources

Combinatorial Hopf algebras from PROs [PDF]

Journal of Algebraic Combinatorics, 2016
We introduce a general construction that takes as input a so-called stiff PRO and that outputs a Hopf algebra. Stiff PROs are particular PROs that can be described by generators and relations with precise conditions.
Bultel, Jean-Paul, Giraudo, Samuele
core   +9 more sources

Commutative combinatorial Hopf algebras [PDF]

Journal of Algebraic Combinatorics, 2006
We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures, and investigate the relations between them.
Hivert, F., Novelli, J. -C., Thibon, J. -Y.   +2 more
core   +9 more sources

Antipode formulas for some combinatorial Hopf algebras

The Electronic Journal of Combinatorics, 2016
Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, Lam and Pylyavskyy studied six combinatorial Hopf algebras that can be thought of as K-theoretic analogues of the Hopf algebras of symmetric functions ...
Patrias, Rebecca
core   +4 more sources

$r-$Bell polynomials in combinatorial Hopf algebras

Comptes Rendus. Mathématique, 2016
We introduce partial $r$-Bell polynomials in three combinatorial Hopf algebras. We prove a factorization formula for the generating functions which is a consequence of the Zassenhauss formula.Comment: 7 ...
Chouria, Ali, Luque, Jean-Gabriel
core   +5 more sources

Combinatorial Hopf algebras in quantum field theory I [PDF]

Reviews in Mathematical Physics, 2004
This manuscript stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Section 1 is the introduction, and contains as well an elementary invitation to the subject.
't Hooft G., Abramowitz M., Bollini C. G., Brouder Ch., Burum D. P., Caianello E. R., Connes A., Connes A., de Lagrange J.-L., Dixmier J., Dür A., Ebrahimi-Fard K., Figueroa H., Figueroa H., Foissy L., Haiman M., Henrici P., Hochschild G., Hochschild G., Hofmann K. H., HÉCTOR FIGUEROA, Itzykson C., JOSÉ M. GRACIA-BONDÍA, Kastler D., Leslie J., Loday J. L., Manoukian E. B., Oeckl R., Reutenauer Ch., Rybnikov K., Schmitt W. R.   +30 more
core   +4 more sources

Bell polynomials in combinatorial Hopf algebras

, 2016
Partial multivariate Bell polynomials have been defined by E.T. Bell in 1934. These polynomials have numerous applications in Combinatorics, Analysis, Algebra, Probabilities, etc.
Aboud, Ammar, Bultel, Jean-Paul, Chouria, Ali, Luque, Jean-Gabriel, Mallet, Olivier   +4 more
core   +3 more sources

Superization and (q,t)-specialization in combinatorial Hopf algebras [PDF]

The Electronic Journal of Combinatorics, 2008
We extend a classical construction on symmetric functions, the superization process, to several combinatorial Hopf algebras, and obtain analogs of the hook-content formula for the (q,t)-specializations of various bases.
Novelli, Jean-Christophe, Thibon, Jean-Yves   +1 more
core   +6 more sources

Convolution Powers of the Identity [PDF]

Discrete Mathematics & Theoretical Computer Science, 2013
We study convolution powers $\mathtt{id}^{\ast n}$ of the identity of graded connected Hopf algebras $H$. (The antipode corresponds to $n=-1$.) The chief result is a complete description of the characteristic polynomial - both eigenvalues and ...
Marcelo Aguiar, Aaron Lauve
doaj   +1 more source