Introducing the permutations package
A 'permutation' is a bijection from a finite set to itself. Permutations are important and interesting objects in a range of mathematical contexts including group theory, recreational mathematics, and the study of symmetry. This short talk will introduce the 'permutations' R package for manipulation and display of permutations. The package has been used for teaching pure mathematics, and contains a number of illustrative examples. The package is fully vectorized and is intended to provide R-centric functionality in the context of elementary group theory. The package includes functionality for working with the "megaminx", a dodecahedral puzzle with similar construction to the Rubik cube; the megaminx puzzle is a pleasing application of group theory and the package was written specifically to analyze the megaminx. From a group-theoretic perspective, the center of the megaminx group comprises a single non-trivial element, the `superflip'. The superflip has a distinctive and attractive appearance and one computational challenge is to find the shortest sequence that accomplishes the superflip. Previously, the best known result was a superflip of 83 turns, due to Clarke. The presentation will conclude by showing one result of the permutations package: an 82-turn superflip.