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symmetric relation

Overview page. Subjects: Computing.

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

See overview in Oxford Index

symmetric relation

Christopher Clapham and James Nicholson.

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

Christopher Clapham and James Nicholson.

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)

Christopher Clapham and James Nicholson.

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))

Christopher Clapham and James Nicholson.

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 ...

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equivalence relation

Christopher Clapham and James Nicholson.

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

Christopher Clapham and James Nicholson.

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 SL2(ℤ) WITH COEFFICIENTS IN A GEOMETRIC REPRESENTATION

F. Callegaro, F. R. Cohen and M. Salvetti.

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 SL2(ℤ) with local coefficients in a classical geometric representation given by...

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Combinatorial Hopf Algebras and K-Homology of Grassmanians

Thomas Lam and Pavlo Pylyavskyy.

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

Giovanni Felder and Alexander P. Veselov.

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...