منابع مشابه
A Geometric Littlewood-richardson Rule
We describe an explicit geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties so that they break into Schubert varieties. There are no restrictions on the base field, and all multiplicities arising are 1; this is important for applications. This rule should be seen as a generalization of Pieri’s rule to arbitrary Schubert classes, by way of ex...
متن کاملLittlewood–Richardson polynomials
We introduce a family of rings of symmetric functions depending on an infinite sequence of parameters. A distinguished basis of such a ring is comprised by analogues of the Schur functions. The corresponding structure coefficients are polynomials in the parameters which we call the Littlewood–Richardson polynomials. We give a combinatorial rule for their calculation by modifying an earlier resu...
متن کاملSmall 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...
متن کاملLittlewood-richardson Semigroups
This note is an extended abstract of my talk at the workshop on Representation Theory and Symmetric Functions, MSRI, April 14, 1997. We discuss the problem of finding an explicit description of the semigroup LRr of triples of partitions of length ≤ r such that the corresponding Littlewood-Richardson coefficient is non-zero. After discussing the history of the problem and previously known result...
متن کاملInequalities between Littlewood-Richardson coefficients
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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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1993
ISSN: 0195-6698
DOI: 10.1006/eujc.1993.1024