# Cyclotomic Shuffles

@article{Ogievetsky2018CyclotomicS, title={Cyclotomic Shuffles}, author={O. Ogievetsky and Varvara Petrova}, journal={Physics of Particles and Nuclei}, year={2018} }

Analogues of 1-shuffle elements for complex reflection groups of type G(m, 1, n) are introduced. A geometric interpretation for G(m, 1, n) in terms of rotational permutations of polygonal cards is given. We compute the eigenvalues, and their multiplicities, of the 1-shuffle element in the algebra of the group G(m, 1, n). Considering shuffling as a random walk on the group G(m, 1, n), we estimate the rate of convergence to randomness of the corresponding Markov chain. We report on the spectrum…

## One Citation

Progressive Randomization of a Deck of Playing Cards: Experimental Tests and Statistical Analysis of the Riffle Shuffle

- MathematicsOpen Journal of Statistics
- 2019

The question of how many shuffles are required to randomize an initially ordered deck of cards is a problem that has fascinated mathematicians, scientists, and the general public. The two principal…

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