胖阶梯和的斜Schur函数
Skew Schur Functions of Sums of Fat Staircases
摘要：
我们将胖阶梯定义为对应于$(n^{α_n}, {n-1}^{α_{n-1}},..., 1^{α_1})$形式的划分的费勒斯图，其中$α= (α_1,...,α_n)$是这样的图的合成或$180^\circ$旋转。如果一个图的斜Schur函数是胖楼梯Schur函数的线性组合，我们称这个图为胖楼梯之和。我们证明了舒尔积极性的结果，得到每次我们增加了一个总和的脂肪楼梯与歪斜图。我们还确定的条件下，图可以是脂肪楼梯的总和，包括充要条件的特殊情况下，当图是一个脂肪楼梯斜单行或列。
英文摘要：
We define a fat staircase to be a Ferrers diagram corresponding to a partition of the form $(n^{α_n}, {n-1}^{α_{n-1}},..., 1^{α_1})$, where $α= (α_1,...,α_n)$ 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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