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The unknot, also called the trivial knot (Rolfsen 1976, p. 51), is a closed loop that is not knotted. In the 1930s Reidemeister first proved that knots exist which are ...

A vector derivative is a derivative taken with respect to a vector field. Vector derivatives are extremely important in physics, where they arise throughout fluid mechanics, ...

Wang's conjecture states that if a set of tiles can tile the plane, then they can always be arranged to do so periodically (Wang 1961). The conjecture was refuted when Berger ...

There are a number of graphs associated with T. I. (and C. T.) Zamfirescu. The Zamfirescu graphs on 36 and 75 vertices, the former of which is a snark, appear in Zamfirescu ...

Discrete Mathematics

An Abelian semigroup is a set whose elements are related by a binary operation (such as addition, rotation, etc.) that is closed, associative, and commutative. A mathematical ...

If one root of the equation f(x)=0, which is irreducible over a field K, is also a root of the equation F(x)=0 in K, then all the roots of the irreducible equation f(x)=0 are ...

The law appearing in the definition of Boolean algebras and lattice which states that a ^ (a v b)=a v (a ^ b)=a for binary operators v and ^ (which most commonly are logical ...

An abstract group is a group characterized only by its abstract properties and not by the particular representations chosen for elements. For example, there are two distinct ...

A golden rhombohedron is a trigonal trapezohedron (and therefore rhombohedron with congruent rhombic faces) whose faces consist of six equal golden rhombi. There are two ...