Skew Schur Functions of Sums of Fat Staircases

Details Skew Schur Functions of Sums of Fat Staircases Skew Schur Functions of Sums of Fat Staircases

2010-03-08

arxiv.org/abs/1003.1691v1

Mathematics

Combinatorics

26 pages

Scientific paper

We define a fat staircase to be a Ferrers diagram corresponding to a partition of the form $(n^{\alpha_n}, {n-1}^{\alpha_{n-1}},..., 1^{\alpha_1})$, where $\alpha = (\alpha_1,...,\alpha_n)$ is a composition, or the $180^\circ$ rotation of such a diagram. If a diagram's skew Schur function is a linear combination of Schur functions of fat staircases, we call the diagram a sum of fat staircases. We prove a Schur-positivity result that is obtained each time we augment a sum of fat staircases with a skew diagram. We also determine conditions on which diagrams can be sums of fat staircases, including necessary and sufficient conditions in the special case when the diagram is a fat staircase skew a single row or column.

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