Promotion and rowmotion
Promotion and rowmotion
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促销和行动
DOI：
10.1016/j.ejc.2012.05.003
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
N. Williams
中科院分区：
文献类型：
--
作者：
Jessica Striker;N. Williams
给出了偏序集序理想上的两个作用--提升和行运动--之间的等变双射。这个双射同时推广了R. Stanley关于两个不相交链的线性扩张的推广的一个结果，以及D. Armstrong、C. Stump和H.托马斯关于非交叉和非嵌套划分的最近工作的某些情况。我们将这种双射应用到几类偏序集上，得到了旋转下各种已知对象的等变双射。我们推广了同样的思想，给出了交替符号矩阵在行运动和B. Wieland回转下的等变双射。最后，我们在交替符号矩阵和全对称自补平面剖分上定义了两个具有相关阶的作用。
We present an equivariant bijection between two actions—promotion and rowmotion—on order ideals in certain posets. This bijection simultaneously generalizes a result of R. Stanley concerning promotion on the linear extensions of two disjoint chains and certain cases of recent work of D. Armstrong, C. Stump, and H. Thomas on noncrossing and nonnesting partitions. We apply this bijection to several classes of posets, obtaining equivariant bijections to various known objects under rotation. We extend the same idea to give an equivariant bijection between alternating sign matrices under rowmotion and under B. Wieland’s gyration. Finally, we define two actions with related orders on alternating sign matrices and totally symmetric self-complementary plane partitions.