University of Miami
Department of Mathematics
Lecture Series
Spring Semester 2020
Some Significant Combinatorial Sequences
presented by
Professor Richard Stanley
Arts and Sciences Distinguished Scholar
University of Miami
5:00pm
Tuesday, February 25, 2020, Ungar Building, Room 402
Tuesday, March 3, 2020, Ungar Building, Room 402
Tuesday, March 17, 2020, [CANCELED]
Tuesday, March 24, 2020, Online
Tuesday, March 31, 2020, Online
Tuesday, April 7, 2020, Online
Tuesday, April 14, 2020, Online
Abstract
Combinatorics is replete with sequences of positive integers that spill over into many other areas. We will survey the basic properties of some of these sequences, focusing on their enumerative properties and their connections with algebra and geometry. These sequences include the following:
| Fibonacci numbers |
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... |
| Euler numbers |
1, 2, 5, 16, 61, 272, 1385, 7936, 50521, ... |
| Catalan numbers |
1, 2, 5, 14, 42, 132, 429, 1430, 4862, ... |
| (n+1)^{n-1} |
1, 1, 3, 16, 125, 1296, 16807, 262144, ... |
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.
