## 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 ...

## 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*.

## 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...## Symmetric Chain Decomposition for Cyclic Quotients of Boolean Algebras and Relation to Cyclic Crystals

in** International Mathematics Research Notices**

January 2013; p ublished online January 2012 .

Journal Article. Subjects: Mathematics. 3439 words.

The quotient of a Boolean algebra by a cyclic group is proved to have a symmetric chain decomposition. This generalizes earlier work of Griggs, Killian and Savage on the case of prime...

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** » ** abstract

## non-symmetric

Overview page. Subjects: Mathematics.

(of a relation)

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...

## 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.

## Mechanical control systems on Lie algebroids

in** IMA Journal of Mathematical Control and Information**

December 2004; p ublished online December 2004 .

Journal Article. Subjects: Mathematics. 0 words.

This paper considers control systems defined on Lie algebroids. After deriving basic controllability tests for general control systems, we specialize our discussion to the class of...

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** » ** abstract

## Commensurability and Representation Equivalent Arithmetic Lattices

in** International Mathematics Research Notices**

January 2014; p ublished online January 2013 .

Journal Article. Subjects: Mathematics. 5704 words.

Prasad and Rapinchuk defined a notion of weakly commensurable lattices in a semisimple group, and gave a classification of weakly commensurable Zariski dense subgroups. A motivation was to...

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** » ** abstract

##
Fusion products, cohomology of GL_{
N
} flag manifolds, and Kostka polynomials

in** International Mathematics Research Notices**

January 2004; p ublished online January 2004 .

Journal Article. Subjects: Mathematics. 0 words.

We explain the relation between the fusion product of symmetric power [math] evaluation modules, as defined by Feigin and Loktev, and the graded coordinate ring *R*
_{μ} which...

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** » ** abstract

## asymmetric relation

Overview page. Subjects: Computing.

A relation *R* defined on a set *S* and having the property that

whenever *x R y*

then it is never the case that

*y R x*

where *x*null...

## antisymmetric relation

Overview page. Subjects: Computing.

A relation *R* defined on a set *S* and having the property that

whenever *x R y* and *y R x*

then *x* = *y*

where *x* and *y* are arbitrary members of *S*....

## equivalence relation

Overview page. Subjects: Mathematics — Philosophy.

A relation that is transitive, symmetric, and reflexive. The concept is a convenient generalization or abstraction of equality. It covers most notions of equals, equivalence, and similarity...

## On Indistinguishability and Prototypes

in** Logic Journal of the IGPL**

September 2003; p ublished online September 2003 .

Journal Article. Subjects: Logic. 0 words.

Tolerance spaces are sets equipped with a reflexive, symmetric, but not necessarily transitive, relation of indistinguishability, and are useful for describing vagueness based on error-prone...

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** » ** abstract

##
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...

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** » ** abstract

## coroutine

Overview page. Subjects: Computing.

A program component that allows structuring of a program in an unusual way. A coroutine resembles a subroutine, with one important difference. A subroutine has a subordinate position...

## Exchangeability and regression models

in** Celebrating Statistics**

September 2005; p ublished online September 2007 .

Chapter. Subjects: Probability and Statistics. 13199 words.

This chapter explores the relation between exchangeability, a concept from stochastic processes, and regression models in which the observed process is modulated by a covariate. A...

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** » ** 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...