Category:Definitions/Euler-Poincaré Characteristic

This category contains definitions related to Euler-Poincaré Characteristic.
Related results can be found in Category:Euler-Poincaré Characteristic.

Let $K$ be a simplicial complex.

The Euler-Poincaré characteristic of $K$ is defined and denoted:

$\map \chi K = \ds \sum_{n \mathop \ge 0} \paren {-1}^n \alpha_n$

where $\alpha_n$ denotes the number of $n$-simplexes of $K$.