论文标题
矩形和月亮多诺群岛中的分段线性促销和RSK
Piecewise-linear promotion and RSK in rectangles and moon polyominoes
论文作者
论文摘要
我们研究了Schützenberger促销，疏散以及根据开关定义的RSK对应关系的分段线性和异性升降机。利用这一观点，我们证明，矩形中的某些链统计在这些地图的作用下可以预测。然后，我们使用它来构建Rubey的Bixtions的分段线性和异性版本之间的等效月亮多诺群落的填充物之间保留这些链条统计，并且我们表明这些地图形成了通勤图。我们还讨论了这些结果如何意味着Ehrhart等效性和Ehrhart Quasi-Poly-Poly-Poly-Poly-Poly-Poly-Poly-Poly-Poly-Poly-Poly-Poly-Polightecial Accolapse of Moon Polyominoes的某些类似物的某些类似物。
We study piecewise-linear and birational lifts of Schützenberger promotion, evacuation, and the RSK correspondence defined in terms of toggles. Using this perspective, we prove that certain chain statistics in rectangles shift predictably under the action of these maps. We then use this to construct piecewise-linear and birational versions of Rubey's bijections between fillings of equivalent moon polyominoes that preserve these chain statistics, and we show that these maps form a commuting diagram. We also discuss how these results imply Ehrhart equivalence and Ehrhart quasi-polynomial period collapse of certain analogues of chain polytopes for moon polyominoes.
