University of Miami
Department of Mathematics
Lecture Series
Spring Semester 2025
Two Difficult Enumeration Problems
presented by
Professor Richard Stanley
Arts and Sciences Distinguished Scholar
University of Miami
Ungar Building Room 411
3:00pm - 4:00pm
Monday, February 3, 2025
Monday, February 10, 2025
Monday, February 17, 2025
Monday, February 24, 2025
Monday, March 3, 2025
Monday, March 17, 2025
Abstract
We will discuss two enumeration problems: (1) enumeration of ordered degree sequences of simple graphs on the vertices 1,2,...,n, and (2) enumeration of n-element labeled interval orders using intervals of generic lengths. Both problems involve some interesting generating function techniques. The first problem also uses the theory of zonotopes, while the second uses the theory of hyperplane arrangments.
Richard P. Stanley
Member of the National Academy of Sciences
Richard Stanley has been a College of Arts and Sciences Distinguished Scholar in Mathematics at the University of Miami since 2014. He was the Norman Levinson Professor of Applied Mathematics at MIT and has been Professor Emeritus there since 2018. Professor Stanley's pioneering contributions to combinatorics and its connections with other areas of mathematics revolutionized the field. He was awarded the George Pólya Prize in Applied Combinatorics in 1975 from the Society of Industrial and Applied Mathematics, the Leroy P. Steele Prize in 2001 from the American Mathematical Society, and the Rolf Schock Prize in Mathematics in 2003 from the Royal Swedish Academy of Sciences. Professor Stanley held a Guggenheim Fellowship and is a fellow of the American Academy of Arts & Sciences and a member of the National Academy of Sciences. Most recently, he is the recipient of the 2022 AMS Leroy P. Steele Prize for Lifetime Achievement.
