About: Stanley symmetric function

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In mathematics and especially in algebraic combinatorics, the Stanley symmetric functions are a family of symmetric functions introduced by Richard Stanley in his study of the symmetric group of permutations. reduced decompositions. (Here denotes the binomial coefficient n(n − 1)/2 and ! denotes the factorial.)

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  • In mathematics and especially in algebraic combinatorics, the Stanley symmetric functions are a family of symmetric functions introduced by Richard Stanley in his study of the symmetric group of permutations. Formally, the Stanley symmetric function Fw(x1, x2, ...) indexed by a permutation w is defined as a sum of certain fundamental quasisymmetric functions. Each summand corresponds to a reduced decomposition of w, that is, to a way of writing w as a product of a minimal possible number of adjacent transpositions. They were introduced in the course of Stanley's enumeration of the reduced decompositions of permutations, and in particular his proof that the permutation w0 = n(n − 1)...21 (written here in one-line notation) has exactly reduced decompositions. (Here denotes the binomial coefficient n(n − 1)/2 and ! denotes the factorial.) (en)
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  • 31980740 (xsd:integer)
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  • 2570 (xsd:nonNegativeInteger)
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  • 1112372655 (xsd:integer)
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  • Richard P. Stanley (en)
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  • Richard (en)
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  • Stanley (en)
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  • 1984 (xsd:integer)
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  • In mathematics and especially in algebraic combinatorics, the Stanley symmetric functions are a family of symmetric functions introduced by Richard Stanley in his study of the symmetric group of permutations. reduced decompositions. (Here denotes the binomial coefficient n(n − 1)/2 and ! denotes the factorial.) (en)
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  • Stanley symmetric function (en)
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