117 research outputs found
Tensor structure from scalar Feynman matroids
We show how to interpret the scalar Feynman integrals which appear when
reducing tensor integrals as scalar Feynman integrals coming from certain nice
matroids.Comment: 12 pages, corrections suggested by referee
Intersection Cographs and Aesthetics
Cographs are complete graphs with colored lines (edges); in an intersection cograph, the points (vertices) and lines (edges) are labeled by sets, and the line between each pair of points is (or represents) their intersection. This article first presents the elementary theory of intersection cographs: 15 are possible on 4 points; constraints on the triangles and quadrilaterals; some forbidden configurations; and how, under suitable constraints, to generate the points from the lines alone. The mathematical theory is then applied to aesthetics, using set cographs to describe the experience of a person enjoying a picture (Mu Qi), poem (Dickinson), play (Shakespeare), or piece of music (Anna Magdalena Bach)
Removing Twins in Graphs to Break Symmetries
Determining vertex subsets are known tools to provide information about automorphism groups of graphs and, consequently about symmetries of graphs. In this paper, we provide both lower and upper bounds of the minimum size of such vertex subsets, called the determining number of the graph. These bounds, which are performed for arbitrary graphs, allow us to compute the determining number in two different graph families such are cographs and unit interval graphs
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