论文标题
偏斜形状的填充物避免对角线图案
Fillings of skew shapes avoiding diagonal patterns
论文作者
论文摘要
偏斜的形状是两个左上角的合理的弗雷尔（Ferrers）形状的差异，共享相同的左上角。我们研究偏斜形状的整数填充物。作为我们的第一个主要结果，我们表明，对于特定的遗传性偏斜形状，我们称之为无D的形状，避免了$ k $的东北链的填充物进行两次培养，并避免了相同尺寸的东南链。由于Ferrers的形状是无D型形状的子类，因此可以将此结果视为Ferrers形状的先前类似结果的概括。 作为我们的第二个主要结果，我们在任意偏斜形状的01填充之间构建了两次两次填充，避免了东南尺寸为2的东南链，而具有相同形状的01填充，同时避免了尺寸为2的东北链和特定的非平方尺寸子填充。这概括了先前的横向填充结果。
A skew shape is the difference of two top-left justified Ferrers shapes sharing the same top-left corner. We study integer fillings of skew shapes. As our first main result, we show that for a specific hereditary class of skew shapes, which we call D-free shapes, the fillings that avoid a north-east chain of size $k$ are in bijection with fillings that avoid a south-east chain of the same size. Since Ferrers shapes are a subclass of D-free shapes, this result can be seen as a generalization of previous analogous results for Ferrers shapes. As our second main result, we construct a bijection between 01-fillings of an arbitrary skew shape that avoid a south-east chain of size 2, and the 01-fillings of the same shape that simultaneously avoid a north-east chain of size 2 and a particular non-square subfilling. This generalizes a previous result for transversal fillings.
