### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Matthew Russell**, Rutgers University, russell2 {at} math [dot] rutgers [dot] edu)
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Interval-valued partial order rank function

Speaker: **Emilie Hogan**, Pacific Northwest National Laboratory

Date: Thursday, October 30, 2014 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Hierarchical data objects whose mathematical representations are partial orders , e.g., ontologies or taxonomies, are often not graded. However, we still want to be able to talk about a sense of vertical level in the partial order for the purpose of layout or statistical studies. In one of my research projects we introduced a notion of an interval rank function. When a poset is graded the interval rank function becomes the traditional integer-valued rank function. In this talk I will give our definition of general interval rank and the special case of "standard interval rank". I will make a case for standard interval rank over any other interval rank function. I will also discuss how we used experimental mathematics in this project to investigate (1) how the standard interval rank function behaves on average for all small partial orders, (2) how it behaves on random partial orders of larger size, and (3) playing with "measures of gradedness", a concept I will define.

See: http://www.math.rutgers.edu/~russell2/expmath/