Differences of Skew Schur Functions of Staircases with Transposed Foundations

Details Differences of Skew Schur Functions of Staircases with Transposed Foundations Differences of Skew Schur Functions of Staircases with Transposed Foundations

2010-03-08

arxiv.org/abs/1003.1688v1

Mathematics

Combinatorics

33 pages

Scientific paper

We consider the skew diagram $\Delta_n$, which is the $180^\circ$ rotation of the staircase diagram $\delta_n = (n,n-1,n-2,...,2,1)$. We create a staircase with bad foundation by augmenting $\Delta_n$ with another skew diagram, which we call the \textit{foundation}. We consider pairs of staircases with bad foundation whose foundations are transposes of one another. Among these pairs, we show that the difference of the corresponding skew Schur functions is Schur-positive in the case when one of the foundations consists of either a one or two row diagram, or a hook diagram.

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