
06618939
j
2016e.00783
Smith, Michael D.
The parity theorem shuffle.
PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 26, No. 1, 1928 (2016).
2016
Taylor \& Francis, Philadelphia, PA
EN
H45
abstract algebra
permutation
parity
inversion
ropes course
doi:10.1080/10511970.2015.1075787
Summary: The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent statement of the Parity Theorem, replacing ``transposition'' with ``adjacent transposition,'' as well as a proof based on an inversion count technique. To build an intuitive understanding of the concept of inversion and to help students discover the Parity Theorem on their own, this article presents a series of five classroom activities based on the groupbuilding initiative ``Telephone Pole Shuffle.''