Descents, Peaks, and P -partitions Doctor of Philosophy

Descents, Peaks, and P -partitions A dissertation presented to the Faculty of the Graduate School of Arts and Sciences of Brandeis University, Waltham, Massachusetts by T. Kyle Petersen We use a variation on Richard Stanley’s P -partitions to study “Eulerian” descent subalgebras of the group algebra of the symmetric group and of the hyperoctahedral group. In each case we give explicit structure polynomials for orthogonal idempotents (including q-analogues in many cases). Much of the study of descents carries over similarly to the study of peaks, where we replace the use of Stanley’s P -partitions with John Stembridge’s enriched P -partitions.