Hopf algebras on decorated noncrossing arc diagrams

A., Hopf algebra structure of a model quantum field theory, Proceedings of the 26th International Colloquium on Group Theoretical Methods in Physics, New York 2006, Editor: S.

The classes of (labelled) diagrams up to this equivalence (permutations of white - or black - spots among themselves) are naturally represented by unlabelled diagrams and will

Lattice, finite, congruence, join-irreducible, join-dependency, lower bounded, sectionally complemented, minimal pair.. The research of the first author was supported by the NSERC

The first one relates equation (2.2) to one of the most classical notion of combinatorics, namely that of triangulation of an n-gon, while the second describes all positive

Using this, it was proved in [7], [15], [17] that any fusion category is equivalent to the representation category of some algebraic structure generalizing Hopf algebras called a

Then it was proved in [Hayashi,1999], [Szlachanyi,2001], [Ostrik,2003] that any fusion category is equivalent to the representation category of some algebraic structure

Keywords: Combinatorial Hopf algebras, monoids, polynomial realization, hook length formula, generating series, binary trees..

2014 Polymer solutions can be conveniently studied in a grand canonical formalism; in this case, the osmotic pressure, the correlations functions and the concentrations