Enumerating two permutation classes by the number of cycles

Abstract

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.

Keywords

• mathematics - combinatorics
• 05a05, 05a15