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Two figures are homothetic if they are related by a dilation (a dilation is also known as a homothecy). This means that the connectors of corresponding points are concurrent ...

Given a set P with |P|=p elements consisting of c_1 numbers 1, c_2 numbers 2, ..., and c_n numbers n and c_1+c_2+...+c_n=p, find the number of permutations with k-1 rises ...

A set of 15 open problems on Schrödinger operators proposed by mathematical physicist Barry Simon (2000). This set of problems follows up a 1984 list of open problems in ...

An algebra with no nontrivial ideals.

A simple continued fraction is a special case of a generalized continued fraction for which the partial numerators are equal to unity, i.e., a_n=1 for all n=1, 2, .... A ...

A curve is simple if it does not cross itself.

A simple directed graph is a directed graph having no multiple edges or graph loops (corresponding to a binary adjacency matrix with 0s on the diagonal). The number of simple ...

A simple function is a finite sum sum_(i)a_ichi_(A_i), where the functions chi_(A_i) are characteristic functions on a set A. Another description of a simple function is a ...

A simple graph, also called a strict graph (Tutte 1998, p. 2), is an unweighted, undirected graph containing no graph loops or multiple edges (Gibbons 1985, p. 2; West 2000, ...

A simple group is a group whose only normal subgroups are the trivial subgroup of order one and the improper subgroup consisting of the entire original group. Simple groups ...