Signature

[share]

The signature of an algebraic system is the collection of relations and operations
on the basic set of the given algebraic system together with an indication of their arity.

An algebraic system (a universal algebra) with signature Ω is also called an Ω- system (respectively, Ω- algebra).

The signature of a quadratic, or symmetric bilinear, form over an ordered field is
a pair of non-negative integers (p,q),
where p is the positive and q the negative index of inertia of the given form
(see Law of inertia; Quadratic form).

Sometimes the number p−q is called the signature of the form.

https://encyclopediaofmath.org/wiki/Signature

[share]

A signature (in Variety (universal algebra)) is a set, whose elements are called operations,
each of which is assigned a natural number (0, 1, 2,...) called its arity.

Given a signature Sigma and a set V, whose elements are called variables,
a word is a finite planar rooted tree in which each node is labelled by either
a variable or an operation,
such that every node labelled by a variable has no branches away from the root and
every node labelled by an operation o has as many branches away from the root as
the arity of o.

An equational law is a pair of such words; we write the axiom consisting of
the words v and w as v=w

[share]

The signature of a knot is a topological invariant in knot theory.
It may be computed from the Seifert surface.

The signature of the matrix V+V^t thought of as a symmetric bilinear form,
is the signature of the knot K.