## Kassie Archer - Enumerating two permutation classes by the number of cycles

dmtcs:6173 - Discrete Mathematics & Theoretical Computer Science, October 27, 2022, vol. 22 no. 2, Permutation Patterns 2019 - https://doi.org/10.46298/dmtcs.6173
Enumerating two permutation classes by the number of cycles

Authors: Kassie Archer 1

• 1 The University of Texas at Tyler, USA

We enumerate permutations in the two permutation classes $\text{Av}_n(312, 4321)$ and $\text{Av}_n(321, 4123)$ by the number of cycles each permutation admits. We also refine this enumeration with respect to several statistics.

Volume: vol. 22 no. 2, Permutation Patterns 2019
Section: Special issues
Published on: October 27, 2022
Accepted on: September 8, 2022
Submitted on: February 28, 2020
Keywords: Mathematics - Combinatorics,05A05, 05A15