2,516 research outputs found
Problems on Polytopes, Their Groups, and Realizations
The paper gives a collection of open problems on abstract polytopes that were
either presented at the Polytopes Day in Calgary or motivated by discussions at
the preceding Workshop on Convex and Abstract Polytopes at the Banff
International Research Station in May 2005.Comment: 25 pages (Periodica Mathematica Hungarica, Special Issue on Discrete
Geometry, to appear
Feynman Diagrams and Rooted Maps
The Rooted Maps Theory, a branch of the Theory of Homology, is shown to be a
powerful tool for investigating the topological properties of Feynman diagrams,
related to the single particle propagator in the quantum many-body systems. The
numerical correspondence between the number of this class of Feynman diagrams
as a function of perturbative order and the number of rooted maps as a function
of the number of edges is studied. A graphical procedure to associate Feynman
diagrams and rooted maps is then stated. Finally, starting from rooted maps
principles, an original definition of the genus of a Feynman diagram, which
totally differs from the usual one, is given.Comment: 20 pages, 30 figures, 3 table
Equivelar and d-Covered Triangulations of Surfaces. I
We survey basic properties and bounds for -equivelar and -covered
triangulations of closed surfaces. Included in the survey is a list of the
known sources for -equivelar and -covered triangulations. We identify all
orientable and non-orientable surfaces of Euler characteristic
which admit non-neighborly -equivelar triangulations
with equality in the upper bound
. These
examples give rise to -covered triangulations with equality in the upper
bound . A
generalization of Ringel's cyclic series of neighborly
orientable triangulations to a two-parameter family of cyclic orientable
triangulations , , , is the main result of this
paper. In particular, the two infinite subseries and
, , provide non-neighborly examples with equality for
the upper bound for as well as derived examples with equality for the upper
bound for .Comment: 21 pages, 4 figure
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