This website uses features that are not well-supported by your browser. Please consider upgrading to a browser and version that fully supports CSS Grid and the CSS Flexible Box Layout Module.
Sidebar image
NB: A PDF version of this announcement (suitable for posting) is also available.

The peak algebra of the symmetric group

Kathryn Nyman
Willamette University

Thursday, December 1, 2011
007 Kemeny Hall, 4 pm
Tea 3:30 pm, 300 Kemeny Hall

Abstract: A peak of a permutation w in Sn  is a position i  for which wi-1< wi and wi >wi+1. Taking sums of permutations with a common peak set gives rise to a subalgebra of the symmetric group algebra. Peaks of ordinary permutations are closely related to descents of signed permutations, and, as such, we find that this Peak Algebra is intrinsically tied to Solomon's Descent Algebras of Types B  and D.   Related algebras arise by reinterpreting the notion of what constitutes a peak and by grouping permutations based on the number of peaks they contain.

In this talk, we explore some of the properties and structure of these peak algebras and look at applications including those to card shuffling and flag vectors of polytopes.

This talk will be accessible to graduate students.