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Crafty Counting
Mathematics and Computer Science
  • Frank A. Farris, Santa Clara University
Document Type
Publication Date
Mathematical Association of America (MAA)

To count a set means to put it in one-to-one correspondence with a set of integers {1, 2, 3,...,n}. Direct counting is nice, but in complicated situations it pays to be more crafty. A problem with patterns of colored tiles gives us a chance to illustrate a popular counting principle known by various names. We'll call it the Burnside-Cauchy-Frobenius formula. It is also popularly called the Burnside Orbit-Counting Lemma, though wags refer to it as "not Burnside," because it was known long before Burnside was born. Later Pólya generalized the formula, so some readers may recognize this as Pólya Enumeration.

Copyright 2008 Mathematical Association of America. All Rights Reserved. Stable URL
Citation Information
FARRIS, Frank A. "Crafty Counting."Math Horizons, February 2008: 12-15. The article illustrates Burnside orbit-counting in an elementary way. It includes an homage to artist Sol LeWitt.