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A C^infty function is a function that is differentiable for all degrees of differentiation. For instance, f(x)=e^(2x) (left figure above) is C^infty because its nth ...

Combinatorial geometry is a blending of principles from the areas of combinatorics and geometry. It deals with combinations and arrangements of geometric objects and with ...

In general, the word "complement" refers to that subset F^' of some set S which excludes a given subset F. Taking F and its complement F^' together then gives the whole of ...

A labeled binary tree containing the labels 1 to n with root 1, branches leading to nodes labeled 2 and 3, branches from these leading to 4, 5 and 6, 7, respectively, and so ...

A labeled ternary tree containing the labels 1 to n with root 1, branches leading to nodes labeled 2, 3, 4, branches from these leading to 5, 6, 7 and 8, 9, 10 respectively, ...

A group generated by the elements P_i for i=1, ..., n subject to (P_iP_j)^(M_(ij))=1, where M_(ij) are the elements of a Coxeter matrix. Coxeter used the notation [3^(p,q,r)] ...

A 15_3 configuration of 15 lines and 15 points, with three lines through three points, three points on every line, and containing no triangles. It is illustrated above in two ...

A cube 9-compound can be constructed from the vertices of the first dodecahedron 2-compound. It will be implemented in a future version of the Wolfram Language as ...

A Ferrers diagram represents partitions as patterns of dots, with the nth row having the same number of dots as the nth term in the partition. The spelling "Ferrars" (Skiena ...

Let (Omega)_(ij) be the resistance distance matrix of a connected graph G on n nodes. Then Foster's theorems state that sum_((i,j) in E(G)))Omega_(ij)=n-1, where E(g) is the ...