In mathematics, a rigid collection C of mathematical objects (for instance sets or functions) is one in which every c ∈ C is uniquely determined by less information about c than one would expect.
The above statement does not define a mathematical property; instead, it describes in what sense the adjective "rigid" is typically used in mathematics, by mathematicians.
Some examples include: In combinatorics, the term rigid is also used to define the notion of a rigid surjection, which is a surjection
for which the following equivalent conditions hold:[1] This relates to the above definition of rigid, in that each rigid surjection
uniquely defines, and is uniquely defined by, a partition of
Given a rigid surjection
, the partition is defined by
Conversely, given a partition of
min
-ordered partition, the function
defined by
is a rigid surjection.
This article incorporates material from rigid on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.