3:00 p.m., Friday
Stephanie van Willigenburg
The algebra of card shuffling
In 1976 Louis Solomon discovered that when we partition the elements
of a finite Coxeter group W in a certain way and form a formal sum
from the elements in each partition we obtain an algebra, called
the descent algebra of W.
For the most famous family of finite Coxeter groups, the symmetric
groups, it was shown in 1989 by Garsia and Reutenauer that these
algebras have a nice description which allowed much of their
structure to be determined. Moreover, it was shown in 1992 by Bayer
and Diaconis that these algebras are closely related to card shuffling.
In this talk we will introduce the descent algebras of the symmetric
groups, some of their properties, and where else they arise in
This talk will be accessible to graduate students.