Dehn-Sommerville manifolds form a broad class of finite simplicial complexes that the paper claims to endow with Dehn-Sommerville face symmetries, level-set closure, chromatic bound 2q+2, and monoid closure under joins.
Pascal triangle, Stirling numbers and the unique invariance of the Euler characteristic
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abstract
We use some basic properties of binomial and Stirling numbers to prove that the Euler characteristic is, essentially, the unique numerical topological invariant for compact polyhedra which can be expressed as a linear combination of the numbers of faces of triangulations. We obtain this result converting it into an eigenvalue problem.
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Dehn Sommerville Manifolds
Dehn-Sommerville manifolds form a broad class of finite simplicial complexes that the paper claims to endow with Dehn-Sommerville face symmetries, level-set closure, chromatic bound 2q+2, and monoid closure under joins.