Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective set theory Of a
relation R on aset S, having the property that for any two distinctelements of S, at least one is not related to the other via R.
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

As already mentioned, however, most contemporary authors are inclined to construe the relation of material constitution as a sui generis, nonmereological relation, or else to treat constitution itself as identity (hence, given (16), as a limit case of an antisymmetric parthood relation; see e.g. Noonan 1993).

Notice that the relation thus defined is asymmetric (rather than antisymmetric): it doesn't permit any object to be existentially dependent upon itself.

(A world containing such wonders as Borges's Aleph, where parthood is not antisymmetric, might by contrast be finite and yet atomless.)

The Fock operator (represented as a matrix) also contains some off diagonal elements, corresponding to the fact that you can swap the electrons in any two states without really changing anything (except the overall sign of the wave function), due to the fact that the full multielectron state must be antisymmetric.
Everything You Ever Wanted to Know About Quantum Mechanics, But Were Afraid to Ask

For every equation there is a symmetric or antisymmetric equation that link different phenomena.

However any weighted average of a series of numbers, in which the weights are antisymmetric about the central value, gives an estimate of the trend.

The control system went into oscillation 37 myr BP when Antarctica started moving into its present position, the temperature of the ocean and that of the rest of the environment opposing each other in antisymmetric mode.

Back to Wikipedia, this time on fermions: Fermions . . . are particles which form totallyantisymmetric composite quantum states.

Fermions have halfintegral spin and are described by wavefunctions that are antisymmetric in the exchange of two particles, i.e. the wavefunctions change sign when two particles change places, and they follow what is called
Additional background material on the Nobel Prize in Physics 1996

The two particles that are used in this theoretical exploration are in what Christandl calls an "antisymmetric state."
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