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A relation R on a set S is antisymmetric provided that distinct elements are never both related to one another. In other words xRy and yRx together imply that x=y.

An operator A^~ is said to be antiunitary if it satisfies: <A^~f_1|A^~f_2> = <f_1|f_2>^_ (1) A^~[f_1(x)+f_2(x)] = A^~f_1(x)+A^~f_2(x) (2) A^~cf(x) = c^_A^~f(x), (3) where ...

Araya and Wiener (2011) found the two cubic planar hypohamiltonian graphs on 70 and 88 vertices, respectively, illustrated above.

A directed graph is called an arborescence if, from a given node x known as the root vertex, there is exactly one elementary path from x to every other node y.

Suppose that E(G) (the commuting product of all components of G) is simple and G contains a semisimple group involution. Then there is some semisimple group involution x such ...

The group of functions from an object G to itself which preserve the structure of the object, denoted Aut(G). The automorphism group of a group preserves the multiplication ...

The baby monster group, also known as Fischer's baby monster group, is the second-largest sporadic group. It is denoted B and has group order |B| = ...

When working over a collection of fields, the base field is the intersection of the fields in the collection, i.e., the field contained in all other fields.

The Bellman-Ford algorithm is an algorithm for solving the shortest path problem, i.e., finding a graph geodesic between two given vertices. Other algorithms that can be used ...

A knot used to join the ends of two ropes together to form a longer length.