In mathematics, a Young tableau (/tæˈbloʊ,ˈtæbloʊ/; plural: tableaux) is a combinatorial object useful in representation theory and Schubert calculus. It provides a convenient way to describe the group representations of the symmetric and general linear groups and to study their properties. Young tableaux were introduced by Alfred Young, a mathematician at Cambridge University, in 1900.[1][2] 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, G. de B. Robinson, Gian-Carlo Rota, Alain Lascoux, Marcel-Paul Schützenberger and Richard P. Stanley.
^Knuth, Donald E. (1973), The Art of Computer Programming, Vol. III: Sorting and Searching (2nd ed.), Addison-Wesley, p. 48, Such arrangements were introduced by Alfred Young in 1900.
^Young, A. (1900), "On quantitative substitutional analysis", Proceedings of the London Mathematical Society, Series 1, 33 (1): 97–145, doi:10.1112/plms/s1-33.1.97. See in particular p. 133.
In mathematics, a Youngtableau (/tæˈbloʊ, ˈtæbloʊ/; plural: tableaux) is a combinatorial object useful in representation theory and Schubert calculus...
or, rarely, tableaus) may refer to: Tableau, a series of four paintings by Piet Mondrian titled Tableau I through to Tableau IV Tableau vivant, a motionless...
_{k}} . A (standard) Youngtableau of shape λ {\displaystyle \lambda } is a filling of the n {\displaystyle n} cells of the Young diagram with all the...
be identified with semistandard Young tableaux. It was discovered by Donald Knuth (1970) (who called it the tableau algebra), using an operation given...
A tableau vivant (French: [tablo vivɑ̃]; often shortened to tableau; plural: tableaux vivants), French for 'living picture', is a static scene containing...
modules. The Young symmetrizer is named after British mathematician Alfred Young. Given a finite symmetric group Sn and specific Youngtableau λ corresponding...
The partition determines a Young diagram with n boxes. A Youngtableau of shape λ is a way of labelling the boxes of this Young diagram by distinct numbers...
polyhedron Skew-symmetric graph Skew-symmetric matrix Skew tableau, a generalization of Youngtableau Skewness, a measure of the asymmetry of a probability...
partition Rank of a partition Crank of a partition Solid partition YoungtableauYoung's lattice Bell number Bell polynomials Dobinski's formula Cumulant...
introduced by Ian Munro and Hendra Suwanda. A related data structure is the Youngtableau. The height of the structure is approximately n {\displaystyle {\sqrt...
relation on the set of skew standard Young tableaux. A jeu de taquin slide is a transformation where the numbers in a tableau are moved around in a way similar...
tableau (for instance there is a cyclic permutation the cycles the entries of the first row one place forward). A Young tabloid is an orbit of Young tableaux...
with visual representations include, among others Four color theorem, Youngtableau, Permutohedron, Graph theory, Partition of a set. Brain imaging experiments...
on Young tableaux) can be defined in terms of the dominance order on the Young diagrams. For a Youngtableau T to dominate another Youngtableau S, the...
equal-sized complete graphs, and their complements, the Turán graphs. A Youngtableau (pl.: tableaux) is a combinatorial object useful in representation theory...
{\displaystyle \mu } -index of a standard Youngtableau be the sum of the values of b μ {\displaystyle b_{\mu }} over the tableau's descents, ind μ ( T ) = ∑ k ∈...
1873–1952, first class cricketer Alfred Young 1873–1940, mathematician and inventor of the Young diagram and Youngtableau Lieutenant Colonel Richard Annesley...
the order polynomial multiplied by | P | ! . {\displaystyle |P|!.} Youngtableau can be considered as linear extensions of a finite order-ideal in the...
2). In the case of S3 one usually labels this representation by the Youngtableau λ = [ 2 , 1 ] {\displaystyle \lambda =[2,1]} and in the case of C 3...
no 6×6 orthogonal Graeco-Latin square is possible. Alfred Young introduces the Youngtableau. English surgeon and ophthalmologist Edward Treacher Collins...
color, scale or orientation may belong to the same group. A Young diagram or Youngtableau, also called Ferrers diagram, is a finite collection of boxes...
and 80 students. The topics covered in the camp's course include the Youngtableau, knot invariants and Schubert polynomials. Students who have the School...
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