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Multiplicity-free skew Schur functions with full interval support. (English) Zbl 1441.05223
Summary: It is known that the Schur expansion of a skew Schur function runs over the interval of partitions, equipped with dominance order, defined by the least and the most dominant Littlewood-Richardson filling of the skew shape. We characterise skew Schur functions (and therefore the product of two Schur functions) which are multiplicity-free and the resulting Schur expansion runs over the whole interval of partitions, i.e., skew Schur functions having Littlewood-Richardson coefficients always equal to 1 over the full interval.
05E05 Symmetric functions and generalizations
05E10 Combinatorial aspects of representation theory
05A17 Combinatorial aspects of partitions of integers
14N15 Classical problems, Schubert calculus
20C30 Representations of finite symmetric groups
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