Ringing the Changes: An Aural Permutation Group
Ringing the Changes: An Aural Permutation Group
Lucy Dechne
Abstract of article: Change ringing is the British sport of ringing all possible permutations of a set of n tuned bells following six rules. Historically, British bell ringers discovered permutation groups nearly a century before mathematicians. A group of permutations that follows the rules (called an extent) can be created by finding certain cosets of a subgroup of S_n. Creating extents is a fun way of practicing multiplication of permutations and exploring permutation groups, subgroups, the idea of algebraic words, and cosets. A theorem by A. T. White elegantly relates the existence of an extent to the existence of a Hamiltonian circuit in a Cayley graph. Some suggested exercises are given.
About the author: Lucy Dechne is a Professor of Mathematics at Fitchburg State College in Fitchburg, Massachusetts. She received her B.S. in mathematics (with a second major in organ performance) from the University of San Francisco and her M.S. and Ph.D. degrees from the University of California, Riverside. Her activities also include being a professional organist, carillonneur, and composer. When teaching, she enjoys combining her love of music with her love of mathematics.
Other links: web site that has an applet to try out bells.