@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-MTRGFQ82-F
  skos:prefLabel "permutation group"@en, "groupe de permutations"@fr ;
  a skos:Concept ;
  skos:broader psr:-CTG7HR06-2 .

psr:-JM0F4GVV-0
  skos:prefLabel "Young tableau"@en, "tableau de Young"@fr ;
  a skos:Concept ;
  skos:related psr:-CTG7HR06-2 .

psr:-C4XZKP2N-4
  skos:prefLabel "permutation"@en, "permutation"@fr ;
  a skos:Concept ;
  skos:narrower psr:-CTG7HR06-2 .

psr:-CTG7HR06-2
  dc:created "2023-08-18"^^xsd:date ;
  dc:modified "2023-08-18"^^xsd:date ;
  skos:broader psr:-C4XZKP2N-4 ;
  skos:definition """En mathématiques, plus particulièrement en algèbre, le groupe symétrique d'un ensemble <i>E</i> est le groupe des permutations de <i>E</i>, c'est-à-dire des bijections de <i>E</i> sur lui-même. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Groupe_sym%C3%A9trique">https://fr.wikipedia.org/wiki/Groupe_sym%C3%A9trique</a>)"""@fr, """In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric group <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\mathrm {S} _{n}}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <msub>
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="normal">S</mi>
         </mrow>
         <mrow class="MJX-TeXAtom-ORD">
         <mi>n</mi>
         </mrow>
         </msub>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathrm {S} _{n}}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/412f98267cda84a9c8abfee60f7184af3cb1aeb2" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.511ex; height:2.509ex;" alt="\\\\mathrm {S} _{n}"></span> defined over a finite set of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle n}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>n</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle n}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="n"></span> symbols consists of the permutations that can be performed on the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle n}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>n</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle n}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="n"></span> symbols. Since there are <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle n!}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>n</mi>
         <mo>!</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle n!}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bae971720be3cc9b8d82f4cdac89cb89877514a6" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.042ex; height:2.176ex;" alt="n!"></span> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle n}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>n</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle n}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="n"></span> factorial) such permutation operations, the order (number of elements) of the symmetric group <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\mathrm {S} _{n}}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <msub>
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="normal">S</mi>
         </mrow>
         <mrow class="MJX-TeXAtom-ORD">
         <mi>n</mi>
         </mrow>
         </msub>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathrm {S} _{n}}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/412f98267cda84a9c8abfee60f7184af3cb1aeb2" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.511ex; height:2.509ex;" alt="\\\\mathrm {S} _{n}"></span> is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle n!}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>n</mi>
         <mo>!</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle n!}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bae971720be3cc9b8d82f4cdac89cb89877514a6" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.042ex; height:2.176ex;" alt="n!"></span>.
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Symmetric_group">https://en.wikipedia.org/wiki/Symmetric_group</a>)"""@en ;
  skos:narrower psr:-MTRGFQ82-F ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Groupe_sym%C3%A9trique>, <https://en.wikipedia.org/wiki/Symmetric_group> ;
  skos:related psr:-JM0F4GVV-0 ;
  skos:prefLabel "groupe symétrique"@fr, "symmetric group"@en ;
  a skos:Concept ;
  skos:inScheme psr: .

psr: a skos:ConceptScheme .