The pragacz identity and a new algorithm for Littlewood-Richardson coefficients
نویسندگان
چکیده
منابع مشابه
Small Littlewood-Richardson coefficients
We develop structural insights into the Littlewood-Richardson graph, whose number of vertices equals the Littlewood-Richardson coefficient cνλ,μ for given partitions λ, μ and ν. This graph was first introduced in [BI12], where its connectedness was proved. Our insights are useful for the design of algorithms for computing the Littlewood-Richardson coefficient: We design an algorithm for the exa...
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Littlewood-Richardson coefficients are the multiplicities in the tensor product decomposition of two irreducible representations of the general linear group GL(n,C). They have a wide variety of interpretations in combinatorics, representation theory and geometry. Mulmuley and Sohoni pointed out that it is possible to decide the positivity of Littlewood-Richardson coefficients in polynomial time...
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We present a polynomiality property of the Littlewood-Richardson coefficients c λμ . The coefficients are shown to be given by polynomials in λ, μ and ν on the cones of the chamber complex of a vector partition function. We give bounds on the degree of the polynomials depending on the maximum allowed number of parts of the partitions λ, μ and ν. We first express the Littlewood-Richardson coeffi...
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We prove that a conjecture of Fomin, Fulton, Li, and Poon, associated to ordered pairs of partitions, holds for many infinite families of such pairs. We also show that the bounded height case can be reduced to checking that the conjecture holds for a finite number of pairs, for any given height. Moreover, we propose a natural generalization of the conjecture to the case of skew shapes.
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In this paper we investigate Q(n) = Q λ′,μ′ (n) = P ν c(nλ + λ;nμ+ μ, ν) as a function of n and show that Q(n) is bounded above if and only if λ/μ is a partition or rotated partition. Here c(λ;μ, ν) is the LittlewoodRichardson coefficient. So Q(n) counts the number of LR tableaux of shape (nλ + λ)/(nμ + μ) or the total number of irreducible characters in the skew character [(nλ+ λ)/(nμ + μ)]. W...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1991
ISSN: 0898-1221
DOI: 10.1016/0898-1221(91)90079-j