منابع مشابه
Counting Non-Isomorphic Chord Diagrams
Different formulas counting families of non isomorphic chord diagrams are given : planar and toroidal ones and those of maximal genus. These formulas are obtained establishing results on the structure of the automorphism group of diagrams of a given genus.
متن کاملof Chord Diagrams
In this paper we study the enumeration of diagrams of n chords joining 2n points on a circle in disjoint pairs. We establish limit laws for the following three parameters: number of components, size of the largest component, and number of crossings. We also nd exact formulas for the moments of the distribution of number of components and number of crossings. Abstract In this paper we study the ...
متن کاملVassiliev Invariants, Chord Diagrams, and Jacobi Diagrams
The goal of this paper is to understand the topological meaning of Jacobi diagrams in relation to knot theory and finite type knot invariants, otherwise known as Vassiliev invariants. To do so, we will first set up the notions of: the Vassiliev invariant and its respective space, the space of chord diagrams, a weight system on chord diagrams, and Jacobi diagrams and their respective space. Duri...
متن کاملCounting non planar diagrams: an exact formula
We present an explicit solution of a simply stated, yet unsolved, combinatorial problem, of interest both in quantum field theory (Feynman diagrams enumeration, beyond the planar approximation) and in statistical mechanics (high temperature loop expansion of some frustrated lattice spin model). PACS: 02.10.Eb, 02.10.Nj, 05.50.+q ∗e-mail: [email protected] The problem of counting the number of r...
متن کاملGenus Ranges of Chord Diagrams.
A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary circle at the ends of each chord. Variations of this construction are considered...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1998
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(98)00031-0