Pascal triangle, Stirling numbers and the unique invariance of the Euler   characteristic
  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. 
Ana Luz\'on and Manuel A. Mor\'on
math.CO math.GT