منابع مشابه
Hopf algebra of ribbon graphs and renormalization
Connes and Kreimer have discovered the Hopf algebra structure behind the renormalization of Feynman integrals. We generalize the Hopf algebra to the case of ribbon graphs, i.e. to the case of theories with matrix fields. The Hopf algebra is naturally defined in terms of surfaces corresponding to ribbon graphs. As an example, we discuss the renormalization of Φ4 theory and the 1/N expansion.
متن کاملExpansions for the Bollobás-riordan Polynomial of Separable Ribbon Graphs
We define 2-decompositions of ribbon graphs, which generalise 2-sums and tensor products of graphs. We give formulae for the Bollobás-Riordan polynomial of such a 2-decomposition, and derive the classical Brylawski formula for the Tutte polynomial of a tensor product as a (very) special case. This study was initially motivated from knot theory, and we include an application of our formulae to m...
متن کاملOn the Ribbon Graphs of Links in Real Projective Space
Every link diagram can be represented as a signed ribbon graph. However, different link diagrams can be represented by the same ribbon graphs. We determine how checkerboard colourable diagrams of links in real projective space, and virtual link diagrams, that are represented by the same ribbon graphs are related to each other. We also find moves that relate the diagrams of links in real project...
متن کاملSynopsis: Dual Equivalence Graphs, Ribbon Tableaux and Macdonald Polynomials
The primary focus of this dissertation is symmetric function theory. The main objectives are to present a new combinatorial construction which may be used to establish the symmetry and Schur positivity of a function expressed in terms of monomials, and to use this method to find a combinatorial description of the Schur expansion for two important classes of symmetric functions, namely LLT and M...
متن کاملExcluded Minors and the Ribbon Graphs of Knots
In this paper we consider minors of ribbon graphs (or, equivalently, cellularly embedded graphs). The theory of minors of ribbon graphs differs from that of graphs in that contracting loops is necessary and doing this can create additional vertices and components. Thus the ribbon graph minor relation is incompatible with the graph minor relation. We discuss excluded minor characterisations of m...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2012
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216512400020