Speaker: Jessica Striker, University of Minnesota

Title: Posets, bijections, and alternating sign matrices

Abstract: In this talk, we will begin with a motivating open problem of finding an explicit bijection between alternating sign matrices and certain plane partitions, giving the solution in a special case. We will put this problem into a larger context by looking at the posets associated to these objects as members of a larger family of tetrahedral posets. We will further broaden our perspective by giving an equivariant bijection between two actions we call promotion and rowmotion on an even more general family of posets. This bijection simultaneously generalizes a result of Stanley concerning promotion and recent work of Armstrong, Stump, and Thomas on root posets and noncrossing partitions. Applying this bijection to various classes of posets translates a complicated poset action into a simple rotation. If time permits, we will revisit the original motivating problem from this new perspective.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491