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An n-route is defined as a walk of length n with specified initial point in which no line succeeds itself.

A generalization of the Gaussian sum. For p and q of opposite parity (i.e., one is even and the other is odd), Schaar's identity states ...

A functor which defines an equivalence of module categories.

Let a sequence {a_i}_(i=1)^infty be strictly increasing and composed of nonnegative integers. Call A(x) the number of terms not exceeding x. Then the density is given by ...

An operator T which commutes with all shift operators E^a, so TE^a=E^aT for all real a in a field. Any two shift-invariant operators commute.

An operator E such that E^ap(x)=p(x+a).

Let f(1)=1, and let f(n) be the number of occurrences of n in a nondecreasing sequence of integers. then the first few values of f(n) are 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, ... ...

A local source is a node of a directed graph with no entering edges (Borowski and Borwein 1991, p. 401; left figure), and a global source (often simply called a source) is a ...

A graphical partitioning based on the eigenvalues and eigenvectors of the Laplacian matrix of a graph.

A polynomial which is not necessarily an invariant of a link. It is related to the dichroic polynomial. It is defined by the skein relationship ...