Pólya's Enumeration Theorem by Example

Summary

Editors' Note: Alan Tucker was born into a mathematical family. His grandfather on his mother's side was David Raymond Curtiss, longtime Professor of Mathematics at Northwestern University and author of the second of the MAA's Carus Monographs, Analytic Functions of a Complex Variable (1926). Alan Tucker's father was Albert Tucker, an eminent mathematician at Princeton for many years, and his uncle was John Curtiss of Johns Hopkins and Miami, one-time executive director of the American Mathematical Society. His stepfather was E. F. Beckenbach at UCLA, and his brother is Thomas Tucker, on the faculty at Colgate University. Beckenbach played a role in the rescue of Mathematics Magazine in 1945.

Alan Tucker is a Distinguished Teaching Professor in the Department of Applied Mathematics and Statistics at the State University of New York in Stony Brook. He was an undergraduate at Harvard and took his PhD at Stanford University in 1969, writing his dissertation under the direction of George Dantzig and D. R. Fulkerson. He was also a teaching assistant for George Pólya in a course in combinatorics and was much influenced by him. Here he discusses Pólya's enumeration theorem. This effort may well have been part of planning that went into Tucker's writing his classic text, Applied Combinatorics (Wiley, 1980), which has been one of most popular combinatorics texts over the past couple of decades. His other books include A Unified Introduction to Linear Algebra: Models, Methods, and Theory (Macmillan, 1988) and Linear Algebra (Macmillan, 1994).