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The edge set of a graph is simply a set of all edges of the graph. The cardinality of the edge set for a given graph g is known as the edge count of g. The edge set for a ...

For any integers a_i with 1<=a_1<a_2<...<a_k<=n, the proportion of permutations in the symmetric group S_n whose cyclic decompositions contain no cycles of lengths a_1, a_2, ...

An endomorphism is called ergodic if it is true that T^(-1)A=A implies m(A)=0 or 1, where T^(-1)A={x in X:T(x) in A}. Examples of ergodic endomorphisms include the map X->2x ...

An array of "trees" of unit height located at integer-coordinate points in a point lattice. When viewed from a corner along the line y=x in normal perspective, a quadrant of ...

A graph vertex in a graph is said to be an even node if its vertex degree is even.

If at least one solution can be determined for a given problem, a solution to that problem is said to exist. Frequently, mathematicians seek to prove the existence of ...

A phrase used by Tukey to describe data points which are outside the outer fences.

A distribution which arises in the study of half-integer spin particles in physics, P(k)=(k^s)/(e^(k-mu)+1). (1) Its integral is given by int_0^infty(k^sdk)/(e^(k-mu)+1) = ...

A knot or link L^n in S^(n+2) is said to be fibered if there exists a fibration f:S^(n+2)-L->S^1 and if the fibration is well-behaved near L (Rolfsen 1976, p. 323). Examples ...

The fitting subgroup is the subgroup generated by all normal nilpotent subgroups of a group H, denoted F(H). In the case of a finite group, the subgroup generated will itself ...