## symmetric relation

Overview page. Subjects: Computing.

A binary relation ∼ on a set *S* is symmetric if, for all *a* and *b* in *S*, whenever *a* ∼ *b* then *b* ∼ *a*.

## symmetric relation

in** The Concise Oxford Dictionary of Mathematics**

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 28 words.

A *binary relation ∼ on a set *S* is symmetric if, for all *a* and *b* in *S*,

## symmetric relation

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 29 words.

A *binary relation ∼ on a set *S* is symmetric if, for all *a* and *b* in *S*, whenever ...

## non-symmetric (of a relation)

in** The Concise Oxford Dictionary of Mathematics**

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 58 words.

Not *symmetric, or *asymmetric, or *antisymmetric. The relation has to hold for some pairs

## non‐symmetric ((of a relation))

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 61 words.

Not *symmetric, or *asymmetric, or *antisymmetric. The relation has to hold for some pairs in both orders, and hold for only one order for some other pairs, i.e. there exist elements ...

null...## equivalence relation

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 62 words.

A *binary relation ~ on a set *S* that is *reflexive, *symmetric and *transitive. For an equivalence relation ~, ...

## equivalence relation

in** The Concise Oxford Dictionary of Mathematics**

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 56 words.

A *binary relation ~ on a set *S* that is *reflexive, *symmetric and *transitive.

##
THE COHOMOLOGY OF THE BRAID GROUP *B*
_{3} AND OF SL_{2}(ℤ) WITH COEFFICIENTS IN A GEOMETRIC REPRESENTATION

in** The Quarterly Journal of Mathematics**

September 2013; p ublished online June 2013 .

Journal Article. Subjects: Pure Mathematics. 0 words.

The purpose of this article is to describe the integral cohomology of the braid group *B*
_{3} and SL_{2}(ℤ) with local coefficients in a classical geometric representation given by...

Go to
** » ** abstract

##
Combinatorial Hopf Algebras and *K*-Homology of Grassmanians

in** International Mathematics Research Notices**

January 2007; p ublished online January 2007 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 0 words.

Motivated by work of Buch on set-valued tableaux in relation to the *K*-theory of the Grassmannian, we study six combinatorial Hopf algebras. These Hopf algebras can be thought of as *K*-theore...

## Polynomial Solutions of the Knizhnik–Zamolodchikov Equations and Schur–Weyl Duality

in** International Mathematics Research Notices**

January 2007; p ublished online January 2007 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 0 words.

An integral formula for the solutions of Knizhnik–Zamolodchikov (KZ) equation with values in an arbitrary irreducible representation of the symmetric group *S*
_{
Nnull...}