Alec Mertin
Visiting Assistant Professor
Mathematics and Statistics Department
Skidmore College
Rowmotion and Homomesy
Simple rules can
sometimes give rise to unexpectedly rich and structured behavior. In this talk,
I will discuss one such example from dynamical algebraic combinatorics,
a growing area that studies what happens when combinatorial objects are repeatedly
transformed. A central idea in this field is homomesy, introduced by
Propp and Roby, which relays a simple truth: although a system may evolve in a
complicated way, certain quantities can exhibit the same average value over
time.
I will focus on rowmotion,
an operation on order ideals of a partially ordered set, and show how homomesy
appears in this setting through concrete examples. I will show a variety of
results, open questions, and future directions.
The talk will be accessible to
students who have taken Linear Algebra.