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A maximal independent set is an independent set which is a maximal set, i.e., an independent set that is not a subset of any other independent set. The generic term "maximal ...

A set X is said to be nowhere dense if the interior of the set closure of X is the empty set. For example, the Cantor set is nowhere dense. There exist nowhere dense sets of ...

Define the harmonic mean of the divisors of n H(n)=(sigma_0(n))/(sum_(d|n)1/d), where sigma_0(n) is the divisor function (the number of divisors of n). For n=1, 2, ..., the ...

The P versus NP problem is the determination of whether all NP-problems are actually P-problems. If P and NP are not equivalent, then the solution of NP-problems requires (in ...

Proved in 1933. If q is an odd prime or q=0 and n is any positive integer, then there is a Hadamard matrix of order m=2^e(q^n+1), where e is any positive integer such that ...

A hypersphere S^n is parallelizable if there are n vector fields that are linearly independent at each point. There exist only three parallelizable spheres: S^1, S^3, and S^7 ...

A set of residues {a_1,a_2,...,a_(k+1)} (mod n) such that every nonzero residue can be uniquely expressed in the form a_i-a_j. Examples include {1,2,4} (mod 7) and {1,2,5,7} ...

There exist polyhedra which can be plaited (braided). Examples include a plaited cube and plaited icosahedron illustrated above (Pargeter 1959, Wells 1991). In the above ...

A result in control theory. Define H(psi,x,u)=(psi,f(x,u))=sum_(a=0)^npsi_af^a(x,u). Then in order for a control u(t) and a trajectory x(t) to be optimal, it is necessary ...

A prime constellation, also called a prime k-tuple, prime k-tuplet, or prime cluster, is a sequence of k consecutive numbers such that the difference between the first and ...