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Betti numbers are topological objects which were proved to be invariants by Poincaré, and used by him to extend the polyhedral formula to higher dimensional spaces. ...

The word "number" is a general term which refers to a member of a given (possibly ordered) set. The meaning of "number" is often clear from context (i.e., does it refer to a ...

The free part of the homology group with a domain of coefficients in the group of integers (if this homology group is finitely generated).

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

On a compact oriented Finsler manifold without boundary, every cohomology class has a unique harmonic representation. The dimension of the space of all harmonic forms of ...

The Betti numbers of a compact orientable n-manifold satisfy the relation b_i=b_(n-i).

The circuit rank gamma, also denoted mu (Volkmann 1996, Babić et al. 2002) or beta (White 2001, p. 56) and known as the cycle rank (e.g., White 2001, p. 56), (first) graph ...

The chromatic number of a graph G is the smallest number of colors needed to color the vertices of G so that no two adjacent vertices share the same color (Skiena 1990, p. ...

Number Theory

An odd alternating permutation number, more commonly called an Euler number or secant number.