University of Miami
Department of Mathematics
Lecture Series
Spring Semester 2026
Bijective Proofs
presented by
Professor Richard Stanley
Arts and Sciences Distinguished Scholar
University of Miami
Ungar Building Room 506
3:30pm - 4:30pm
Monday, January 26, 2026
Monday, February 2, 2026
Monday, February 9, 2026
Monday, February 16, 2026
Monday, February 23, 2026
Monday, March 2, 2026
Abstract
A fundamental method for showing that two sets have the same number of elements is to construct a bijection (one-to-one correspondence) between them. Such a proof is an important way to determine the number of elements of a finite set and to find unexpected connections among different counting problems.
We will give an introduction to the method of bijective proofs. After discussing the basic concepts, some fundamental techniques, and some simple examples we will give a number of important applications. The lectures will be aimed at graduate students at all levels and even undergraduate math majors. No knowledge of combinatorics is assumed.
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.
