Editing Young tableau (section)

{{Short description|A combinatorial object in representation theory}}
In [[mathematics]], a '''Young tableau''' ({{IPAc-en|t|æ|ˈ|b|l|oʊ|,_|ˈ|t|æ|b|l|oʊ}}; plural: '''tableaux''') is a [[combinatorics|combinatorial]] object useful in [[representation theory]] and [[Schubert calculus]]. It provides a convenient way to describe the [[group representation]]s of the [[symmetric group|symmetric]] and [[general linear group|general linear]] [[Group (mathematics)|groups]] and to study their properties. 

Young tableaux were introduced by [[Alfred Young (mathematician)|Alfred Young]], a [[mathematician]] at [[University of Cambridge|Cambridge University]], in 1900.<ref>{{citation|title=The Art of Computer Programming, Vol. III: Sorting and Searching|first=Donald E.|last=Knuth|author-link=Donald Knuth|edition=2nd|publisher=Addison-Wesley|year=1973|page=48|quote=Such arrangements were introduced by Alfred Young in 1900|title-link=The Art of Computer Programming}}.</ref><ref>{{citation|title=On quantitative substitutional analysis|first=A.|last=Young|journal=Proceedings of the London Mathematical Society|year=1900|volume=33|series=Series 1|issue=1|pages=97–145|doi=10.1112/plms/s1-33.1.97|url=https://zenodo.org/record/1447746}}. See in particular p.&nbsp;133.</ref> They were then applied to the study of the symmetric group by [[Georg Frobenius]] in 1903. Their theory was further developed by many mathematicians, including [[Percy MacMahon]], [[W. V. D. Hodge]], [[Gilbert de Beauregard Robinson|G. de B. Robinson]], [[Gian-Carlo Rota]], [[Alain Lascoux]], [[Marcel-Paul Schützenberger]] and [[Richard P. Stanley]].