On card shuffling, a mathematical menu
Disguised as a menu served in three courses the authors give an entertaining and yet rigorous answer to a question posed by \textit{C. Spleiss} in [Elem. Math. 52, p. 137 (1997)] on the number of perfect shuffles of some deck of cards that results in the original state of the deck. Representing the shuffle as a permutation \(\sigma\) and using some elementary divisibility arguments they determine the minimum \(l\) for which \(\sigma^l\) is the identity. As a `dessert' some extremal values of \(l\) are discussed and a connection to an open conjecture of Artin is mentioned. The authors close with the remark that the result is not new but that they presented it in a `tasty' and easy-to-digest form.
scientific article; zbMATH DE number 1443354