@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:-F7H3K8H1-0
  skos:prefLabel "coefficient binomial"@fr, "binomial coefficient"@en ;
  a skos:Concept ;
  skos:narrower psr:-W24S9MNF-2 .

psr:-W24S9MNF-2
  dc:created "2023-08-24"^^xsd:date ;
  skos:prefLabel "Bernoulli's triangle"@en, "triangle de Bernoulli"@fr ;
  a skos:Concept ;
  skos:broader psr:-F7H3K8H1-0 ;
  skos:definition """<b>Bernoulli's triangle</b> is an array of partial sums of the binomial coefficients. For any non-negative integer <i>n</i> and for any integer <i>k</i> included between 0 and <i>n</i>, the component in row <i>n</i> and column <i>k</i> is given by:  <dl><dd><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 \\\\sum _{p=0}^{k}{n \\\\choose p},}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <munderover>           <mo>∑<!-- ∑ --></mo>           <mrow class="MJX-TeXAtom-ORD">             <mi>p</mi>             <mo>=</mo>             <mn>0</mn>           </mrow>           <mrow class="MJX-TeXAtom-ORD">             <mi>k</mi>           </mrow>         </munderover>         <mrow class="MJX-TeXAtom-ORD">           <mrow>             <mrow class="MJX-TeXAtom-OPEN">               <mo maxsize="2.047em" minsize="2.047em">(</mo>             </mrow>             <mfrac linethickness="0">               <mi>n</mi>               <mi>p</mi>             </mfrac>             <mrow class="MJX-TeXAtom-CLOSE">               <mo maxsize="2.047em" minsize="2.047em">)</mo>             </mrow>           </mrow>         </mrow>         <mo>,</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\sum _{p=0}^{k}{n \\\\choose p},}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4ef2897928882c1272c98f99c0d6288e2f75f30" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:9.205ex; height:7.676ex;" alt="{\\\\displaystyle \\\\sum _{p=0}^{k}{n \\\\choose p},}"> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Bernoulli%27s_triangle">https://en.wikipedia.org/wiki/Bernoulli%27s_triangle</a>)"""@en, """Le triangle de Bernoulli est une présentation en tableau triangulaire des sommes partielles des lignes du triangle de Pascal. Il est répertorié comme suite A008949 de l'OEIS. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Triangle_de_Bernoulli">https://fr.wikipedia.org/wiki/Triangle_de_Bernoulli</a>)"""@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Triangle_de_Bernoulli>, <https://en.wikipedia.org/wiki/Bernoulli%27s_triangle> ;
  skos:inScheme psr: ;
  dc:modified "2024-10-18"^^xsd:date .