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Description: |
A skew-Schur function can be expressed as a sum of Schur functions with non-negative integer multiplicities given by the well-known Littlewood-Richardson coefficients. These coefficients also govern the decomposition of a product of two Schur functions as a sum of Schur functions. Stembridge (2000) has classified the products of Schur functions that are multiplicity-free, that is, those for which every coefficient in the resulting Schur function expansion is 0 or 1. More recently, Thomas, Yong (2005), and Gutschwager (2006) have classified the multiplicity-free skew-Schur functions, and King et al. (2009) have given a meaning for that phenomenon in terms of hives.
The dominance order on partitions has been used in the study of the support of a skew-Schur function. Namely it is contained in the interval defined by the least and the most dominant filling of the skew-shape. Having as starting point the classification of multiplicity-free skew-Schur functions, done independently by Thomas and Yong and by Gutschwager, we classify the multiplicity-free skew-Schur functions whose support is that full interval. This is a joint work with O. Azenhas and A. Conflitti.
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