Pascal triangle, Stirling numbers and the unique invariance of the Euler characteristic

2012/02/03 by Ana Luzón, Luzón, Ana, Manuel A. Morón +1 · 1 citation
Materials Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Liquid Crystal Research Advancements

paper · pdf · doi:10.48550/arxiv.1202.0663

openalex publication_date 2012/02/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Cited by

• Dehn Sommerville Manifolds

Related

• Unusual formulae for the Euler characteristic
• The Euler characteristic of a polyhedron as a valuation on its coordinate vector lattice
• The Euler characteristic of a triangulated manifold in terms of even-dimensional faces
• Two deformed Pascal's triangles and its new properties
• Equivariant Euler characteristics on permutohedral varieties