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...h>R</math> on a [[Set (mathematics)|set]] <math>X</math> is the smallest [[symmetric relation]] on <math>X</math> that contains <math>R.</math> ...the set of humans and <math>R</math> is the relation 'parent of', then the symmetric closure of <math>R</math> is the relation "<math>x</math> is a parent or a ...

...th>X^n:=X \times \cdots \times X</math> by the permutation action of the [[symmetric group]] <math>\mathfrak{S}_n</math>. ...th symmetric power of a vector space ''V'' is the vector subspace of the [[symmetric algebra]] of ''V'' consisting of degree-''n'' elements (here the product is ...

...1</sub>,&nbsp;''u''₂,&nbsp;''u''₃,&nbsp;... with the relations ...em]], by adding the relations ''u''{{su|b=''i''|p=2}}&nbsp;=&nbsp;0 to the relations of the corresponding generalized braid group. ...

...chur polynomial|Schur functions]] as determinants in terms of [[elementary symmetric function]]s. The corresponding identity also holds for Schubert classes. ...and complete symmetric functions, and Schubert classes satisfy these same relations. ...

...is a [[filtered algebra]] generated by degree one elements, with defining relations of degree 2. It was pointed out by [[Yuri Manin]] that such algebras play a ...nerators ''V'' = ''A''₁ and a subspace of homogeneous quadratic relations ''S'' ⊂ ''V'' ⊗ ''V''.<ref>{{cite book |last1=Polishchuk |first1=Alexander ...

...cting on an element of area in the deformed configuration. This tensor is symmetric and is defined via The PK2 stress (<math>\boldsymbol{S}</math>) is symmetric and is defined via the relation ...

...t description|2-parameter family of algebras with the Hecke algebra of the symmetric group as a quotient}} ...Hecke algebras are deformations of the [[group ring|group algebra]] of the symmetric group. ...

{{Short description|French mathematician, developed calculus of relations (1921 to 2013)}} ...cite book|last1=Schmidt|first1=Gunther|last2=Ströhlein|first2=Thomas|title=Relations and Graphs: Discrete Mathematics for Computer Scientists|url={{google books ...

The '''symmetric logarithmic derivative''' is an important quantity in [[quantum metrology]] ...re <math>\rho</math> is [[Self-adjoint operator|Hermitian]] and [[Definite symmetric matrix|positive semi-definite]]. In most applications, <math>\rho</math> an ...

{{Short description|Math relation that is reflexive and symmetric}} ...n''' on an [[algebraic structure]] is a [[reflexive relation|reflexive]] [[symmetric relation]] that is compatible with all operations of the structure. Thus a ...

...ation]]; that is, a [[Reflexive relation|reflexive]], [[Symmetric relation|symmetric]] and [[Transitive relation|transitive]] [[Binary relation|relation]]. [[Category:Binary relations]] ...

...rojective representation]]s of the [[alternating group|alternating]] and [[symmetric group]]s. The covering groups were classified in {{Harv|Schur|1911}}: for ...metric and alternating groups were classified in {{harv|Schur|1911}}. The symmetric group of degree {{nowrap|''n'' ≥ 4}} has ...

...symmetric decreasing rearrangement''' of a function is a function which is symmetric and decreasing, and whose [[level sets]] are of the same size as those of t ...[measurable set]], <math>A,</math> in <math>\R^n,</math> one defines the ''symmetric rearrangement'' of <math>A,</math> called <math>A^*,</math> as the ball cen ...

* {{annotated link|Symmetric closure}} [[Category:Binary relations]] ...

...lity''', named after [[Józef Marcinkiewicz]] and [[Antoni Zygmund]], gives relations between [[Moment (mathematics)|moments]] of a collection of [[independent r ...of Khintchine, Marcinkiewicz&ndash;Zygmund and Rosenthal inequalities for symmetric statistics. ''Scandinavian Journal of Statistics'', 26(4):621&ndash;633, 19 ...

...urvature operator]]s in differential geometry, and the classification of [[symmetric space]]s.<ref name="Nikolayevsky-2003"/> ...all Osserman manifolds either [[flat manifold|flat]] or locally rank-one [[symmetric spaces]]?}} ...

...y, '''countable Borel relations''' are a class of [[Relation (mathematics)|relations]] between [[standard Borel space]] which are particularly well behaved. Thi ...invariant descriptive set theory is the relative complexity of equivalence relations. An equivalence relation <math>E</math> on a set <math>X</math> is consider ...

{{stack|{{Binary relations}}}} ...erial relation|serial]], which is also called total. Similarly, connected relations are sometimes called {{em|{{visible anchor|complete|Complete relation}}}},< ...

...mutative ring generated by all the elements ''g''_''i'' with the relations ...somorphic to the [[ring of symmetric functions]] (or the [[Hopf algebra of symmetric functions]]). ...

...theory]] and corresponding to deformations of the [[canonical commutation relations]]. For other deformations of Gaussian distributions, see [[q-Gaussian distr ...ve, but has a kernel, which leads in these cases to the symmetric and anti-symmetric Fock spaces, respectively. ...