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For a general two-player zero-sum game, max_(i<=m)min_(j<=n)a_(ij)<=min_(j<=n)max_(i<=m)a_(ij). If the two are equal, then write ...

The circumference of a graph is the length of any longest cycle in a graph. Hamiltonian graphs on n>1 vertices therefore have circumference of n. For a cyclic graph, the ...

A group action G×Omega->Omega might preserve a special kind of partition of Omega called a system of blocks. A block is a subset Delta of Omega such that for any group ...

A cycle of a finite group G is a minimal set of elements {A^0,A^1,...,A^n} such that A^0=A^n=I, where I is the identity element. A diagram of a group showing every cycle in ...

A set of generators (g_1,...,g_n) is a set of group elements such that possibly repeated application of the generators on themselves and each other is capable of producing ...

A Hasse diagram is a graphical rendering of a partially ordered set displayed via the cover relation of the partially ordered set with an implied upward orientation. A point ...

A matrix used in the Jacobi transformation method of diagonalizing matrices. The Jacobi rotation matrix P_(pq) contains 1s along the diagonal, except for the two elements ...

The most general form of this theorem states that in a commutative unit ring R, the height of every proper ideal I generated by n elements is at most n. Equality is attained ...

A Lucas chain for an integer n>=1 is an increasing sequence 1=a_0<a_1<a_2<...<a_r=n of integers such that every a_k, k>=1, can be written as a sum a_k=a_i+a_j of smaller ...

Let a module M in an integral domain D_1 for R(sqrt(D)) be expressed using a two-element basis as M=[xi_1,xi_2], where xi_1 and xi_2 are in D_1. Then the different of the ...