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A connected dominating set in a connected graph G is a dominating set in G whose vertices induce a connected subgraph, i.e., one in which there is no dominating vertex not ...

A topological basis is a subset B of a set T in which all other open sets can be written as unions or finite intersections of B. For the real numbers, the set of all open ...

A distance-heredity graph, also known as a completely separable graph, is a graph G such that the distance matrix of every connected vertex-induced subgraph G_V of G is the ...

There exists a positive integer s such that every sufficiently large integer is the sum of at most s primes. It follows that there exists a positive integer s_0>=s such that ...

The improvement of the convergence properties of a series, also called convergence acceleration or accelerated convergence, such that a series reaches its limit to within ...

A polynomial function of the elements of a vector x can be uniquely decomposed into a sum of harmonic polynomials times powers of |x|.

5((x^5)_infty^5)/((x)_infty^6)=sum_(m=0)^inftyP(5m+4)x^m, where (x)_infty is a q-Pochhammer symbol and P(n) is the partition function P.

There are certain optimization problems that become unmanageable using combinatorial methods as the number of objects becomes large. A typical example is the traveling ...

Any linear combination of real spherical harmonics A_lP_l(costheta)+sum_(m=1)^l[A_l^mcos(mphi)+B_l^msin(mphi)]P_l^m(costheta) for l fixed whose sum is not premultiplied by a ...

The number N_d^((b))(n) of digits d in the base-b representation of a number n is called the b-ary digit count for d. The digit count is implemented in the Wolfram Language ...