Document Zbl 1517.05014

Enumerating two permutation classes by the number of cycles. (English) Zbl 1517.05014

Discrete Math. Theor. Comput. Sci. 22(2021-2023), No. 2, Paper No. 11, 12 p. (2022).

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

MSC:

05A15	Exact enumeration problems, generating functions
05A10	Factorials, binomial coefficients, combinatorial functions

Keywords:

pattern avoidance; cycles; permutation statistics; fixed points; excedances; inversions; involutions

Software:

AARON

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References:

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