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Minimal Color Assignments on Pure Simplicial Complexes
Uriel Scott
1917 Potomac Rd, Atlanta, GA 30338, USA
urielscott@urielscott.com
Annals of Combinatorics 6 (3) p.445-461 September, 2002
AMS Subject Classification: 05E99
Abstract:
Given a pure simplicial complex C of dimension d-1, assign a subset of to each vertex, in such a way that each maximal face has all d colors. What is the minimum total number NC(C) of color assignments needed? The number of vertices is a lower bound on NC(C), which is attained if and only if the simplicial complex is completely balanced Thus for any given pure simplicial complex, we have a measure of the extent to which it fails to be completely balanced. We obtain complete solutions for NC(C) in the case where C has four or less facets.
Keywords: balanced simplicial complexes, Noether complexity, linear system of parameters

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