@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: a skos:ConceptScheme .
psr:-GSCJ7V4L-D
  skos:definition """In mathematics, <b>Bhargava's factorial function</b>, or simply <b>Bhargava factorial</b>,  is a certain generalization of the factorial function developed by the Fields Medal winning mathematician Manjul Bhargava as part of his thesis in Harvard University in 1996. The Bhargava factorial has the property that many number-theoretic results involving the ordinary factorials remain true even when the factorials are replaced by the Bhargava factorials. Using an arbitrary infinite subset <i>S</i> of the set <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 \\\\mathbb {Z} }">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow class="MJX-TeXAtom-ORD">           <mi mathvariant="double-struck">Z</mi>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {Z} }</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/449494a083e0a1fda2b61c62b2f09b6bee4633dc" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.176ex;" alt="{\\\\displaystyle \\\\mathbb {Z} }"></span> of integers, Bhargava associated a positive integer with every positive integer <i>k</i>, which he denoted by <i>k</i> !<sub><i>S</i></sub>, with the property that if one takes <i>S</i> = <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 \\\\mathbb {Z} }">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow class="MJX-TeXAtom-ORD">           <mi mathvariant="double-struck">Z</mi>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {Z} }</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/449494a083e0a1fda2b61c62b2f09b6bee4633dc" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.176ex;" alt="{\\\\displaystyle \\\\mathbb {Z} }"></span> itself, then the integer associated with <i>k</i>, that is <i>k</i> !<sub><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 \\\\mathbb {Z} }">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow class="MJX-TeXAtom-ORD">           <mi mathvariant="double-struck">Z</mi>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {Z} }</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/449494a083e0a1fda2b61c62b2f09b6bee4633dc" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.176ex;" alt="{\\\\displaystyle \\\\mathbb {Z} }"></span> </sub>, would turn out to be the ordinary factorial of <i>k</i> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Bhargava_factorial">https://en.wikipedia.org/wiki/Bhargava_factorial</a>)"""@en ;
  skos:altLabel "Bhargava's factorial function"@en ;
  skos:prefLabel "factorielle de Bhargava"@fr, "Bhargava factorial"@en ;
  skos:inScheme psr: ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Bhargava_factorial> ;
  skos:broader psr:-W127WDLN-J ;
  dc:created "2023-08-24"^^xsd:date ;
  a skos:Concept ;
  dc:modified "2024-10-18"^^xsd:date .

psr:-W127WDLN-J
  skos:prefLabel "factorielle"@fr, "factorial"@en ;
  a skos:Concept ;
  skos:narrower psr:-GSCJ7V4L-D .