Promotion and RowmotionAlgebra & Discrete Mathematics
|Start time:||Tue, Apr 24 2012, 2:10PM|
In this talk, I will present an equivariant bijection between two actions---promotion and rowmotion---on order ideals in certain posets. This bijection simultaneously generalizes a result of Stanley concerning promotion on the linear extensions of two disjoint chains and recent work of Armstrong, Stump, and Thomas on root posets and noncrossing partitions. Applying this bijection to several classes of posets yields equivariant bijections to various known objects under rotation. Extending this same idea gives an equivariant bijection between alternating sign matrices under rowmotion and under Wieland's gyration. Lastly, I will define two actions with related orders on alternating sign matrices and totally symmetric self-complementary plane partitions and give some open questions. This is joint work with Nathan Williams.