Mathematics – Combinatorics
Scientific paper
2010-09-21
Mathematics
Combinatorics
Title slightly changed. A section on ribbons has been added. Abstract and Introduction updated accordingly
Scientific paper
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 characterize 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. In addition, a skew Schur function with a disconnected shape attains the full interval only if its components are ribbons. We consider strips, and ribbons made either of columns or rows, and characterise those whose support attains the full interval, i.e. having Littlewood--Richardson coefficients always positive. Schur function products with all Littlewood-Richardson coefficients positive are also classified.
Azenhas Olga
Conflitti Alessandro
Mamede Ricardo
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