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.

References in corpus (4)

• Fixed points and excedances in restricted permutations
• Exact and asymptotic enumeration of cyclic permutations according to descent set
• Cyclic permutations avoiding pairs of patterns of length three
• Enumeration of cyclic permutations in vector grid classes