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Let I(G) denote the set of all independent sets of vertices of a graph G, and let I(G,u) denote the independent sets of G that contain the vertex u. A fractional coloring of ...

A fractional ideal is a generalization of an ideal in a ring R. Instead, a fractional ideal is contained in the number field F, but has the property that there is an element ...

A functional is a real-valued function on a vector space V, usually of functions. For example, the energy functional on the unit disk D assigns a number to any differentiable ...

Given a real m×n matrix A, there are four associated vector subspaces which are known colloquially as its fundamental subspaces, namely the column spaces and the null spaces ...

The interesting function defined by the definite integral G(x)=int_0^xsin(tsint)dt, illustrated above (Glasser 1990). The integral cannot be done in closed form, but has a ...

Let G be a simple connected graph, and take 0<=i<=d(G), where d(G) is the graph diameter. Then G has global parameters c_i (respectively a_i, b_i) if the number of vertices ...

Let there be m doctors and n<=m patients, and let all mn possible combinations of examinations of patients by doctors take place. Then what is the minimum number of surgical ...

For all n, there exists a k such that the kth term of the Goodstein sequence G_k(n)=0. In other words, every Goodstein sequence converges to 0. The secret underlying ...

The graph diameter of a graph is the length max_(u,v)d(u,v) of the "longest shortest path" (i.e., the longest graph geodesic) between any two graph vertices (u,v), where ...

The great rhombicosidodecahedral graph is the Archimedean graph on 120 vertices and 180 edges that is the skeleton of the great rhombicosidodecahedron as well as the uniform ...