773 research outputs found
Structure of the flow and Yamada polynomials of cubic graphs
We establish a quadratic identity for the Yamada polynomial of ribbon cubic
graphs in 3-space, extending the Tutte golden identity for planar cubic graphs.
An application is given to the structure of the flow polynomial of cubic graphs
at zero. The golden identity for the flow polynomial is conjectured to
characterize planarity of cubic graphs, and we prove this conjecture for a
certain infinite family of non-planar graphs.
Further, we establish exponential growth of the number of chromatic
polynomials of planar triangulations, answering a question of D. Treumann and
E. Zaslow. The structure underlying these results is the chromatic algebra, and
more generally the SO(3) topological quantum field theory.Comment: 22 page
Review of AdS/CFT Integrability: An Overview
This is the introductory chapter of a review collection on integrability in
the context of the AdS/CFT correspondence. In the collection we present an
overview of the achievements and the status of this subject as of the year
2010.Comment: 31 pages, v2: reference added, references to other chapters updated,
v3: footnote 1 on location of references added, v4: minor changes, references
added, accepted for publication in Lett. Math. Phys, v5: minor corrections,
links to chapters updated, attached IntAdS.pdf with all chapters in one file,
see http://arxiv.org/src/1012.3982/anc/IntAdS.pdf or
http://www.phys.ethz.ch/~nbeisert/IntAdS.pd
- …