Full support of a class of ribbon shapes and the Schur positivity order on skew shapes
|What||Arbeitsgemeinschaft Diskrete Mathematik|
from 15:15 to 16:45
|Where||TU-Wien, Freihaus (4., Wiedner Hauptstraße 8-10), Dissertantenraum, grüner Turm (A), 8. Stock|
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Olga Azenhas (Universidade de Coimbra)
Abstract. Schur functions are considered to be the most important basis for the ring of symmetric functions. Skew Schur functions are indexed by skew shapes and as symmetric functions they have a linear expansion over Schur functions where the structure coefficients are the Littlewood-Richardson coefficients. Interestingly, the partitions which appear in that expansion fit, in a certain sense, the skew shape and run over a subposet of the dominance lattice of partitions with bottom and top elements determined by that skew shape. I shall discuss some results, in collaboration with Conflitti and Mamede, on criteria for full support of a special class of ribbon shapes, which imply a recent classification of maximal connected skew shapes in the Schur positivity order by McNamara and van Willigenburg.