: Mathématiques: Young's lattice

mathematical analysis > function > symmetric function > Young's lattice

algebra > representation theory > group representation > Young's lattice

mathematical analysis > combinatorics > algebraic combinatorics > Young's lattice

algebra > combinatorics > algebraic combinatorics > Young's lattice

algebra > abstract algebra > algebraic structure > lattice > Young's lattice

Young's lattice

In mathematics, Young's lattice is a lattice that is formed by all integer partitions. It is named after Alfred Young, who, in a series of papers On quantitative substitutional analysis, developed the representation theory of the symmetric group. In Young's theory, the objects now called Young diagrams and the partial order on them played a key, even decisive, role. Young's lattice prominently figures in algebraic combinatorics, forming the simplest example of a differential poset in the sense of Stanley (1988). It is also closely connected with the crystal bases for affine Lie algebras.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Young%27s_lattice)

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