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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.
MSC:
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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