Department of Mathematics Calendar
Joshua Hallam, Wake Forest University, Whitney duals of graded partially ordered sets
October 2 | 3:00 pm - 4:00 pm EDT
To each graded poset one can associate two sequences of numbers; the Whitney numbers of the first kind and the Whitney numbers of the second kind. One sequence keeps track of the Möbius function at each rank level and other keeps track of the number of elements at each rank level.
We say two posets P and Q are Whitney duals of each other if the absolute value of the Whitney numbers of the first kind of P is the Whitney numbers of the second kind of Q and vice-versa. In this talk, we will describe a method to construct Whitney duals. This method uses edge labelings and quotient posets. We will also discuss some examples of posets which have Whitney duals. The edge labelings we use to construct Whitney duals allow us to define an action of the 0-Hecke algebra on the maximal chains of posets with these labelings. Time permitting, we will discuss this action.
No prior knowledge of Whitney numbers, edge labelings, or quotient posets will be assumed. This is joint work with Rafael S. González D’león.