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Markov's theorem states that equivalent braids expressing the same link are mutually related by successive applications of two types of Markov moves. Markov's theorem is ...

The Markström graph is a cubic planar graph on 24 vertices which lacks cycles of length 4 and 8 but contains cycles of length 16. (In particular, it contains cycles of ...

If a group of men and women may date only if they have previously been introduced, then a complete set of dates is possible iff every subset of men has collectively been ...

A sequence of random variates X_0, X_1, ... with finite means such that the conditional expectation of X_(n+1) given X_0, X_1, X_2, ..., X_n is equal to X_n, i.e., ...

The "mathematical paradigm" is a term that may be applied to the fundamental idea that events in the world can be described by mathematical equations, and that solutions to ...

All Mathieu functions have the form e^(irz)f(z), where f(z) has period 2pi and r is known as the Mathieu characteristic exponent. This exponent is returned by the Wolfram ...

The Mathon graphs are three strongly regular graphs on 784 vertices with regular parameters as summarized in the following tables. k spectrum regular parameters 0 ...

An n×m matrix A^- is a 1-inverse of an m×n matrix A for which AA^-A=A. (1) The Moore-Penrose matrix inverse is a particular type of 1-inverse. A matrix equation Ax=b (2) has ...

Nonhomogeneous matrix equations of the form Ax=b (1) can be solved by taking the matrix inverse to obtain x=A^(-1)b. (2) This equation will have a nontrivial solution iff the ...

A maximal ideal of a ring R is an ideal I, not equal to R, such that there are no ideals "in between" I and R. In other words, if J is an ideal which contains I as a subset, ...