Pattern-restricted one-cycle permutations with a pattern-restricted cycle form
Kassie Archer, Ethan Borsh, Jensen Bridges, Christina M. Graves, Millie Jeske · Enumerative Combinatorics and Applications · 2024
In this paper, we consider permutations composed of one cycle that avoid the monotone decreasing permutation k(k -1) . . .21, whose cycle form also demonstrates some pattern avoidance.If the cycle is written in the form with 1 appearing at the beginning of the cycle and this form avoids a pattern of length 3, we find answers in terms of continued fraction generating functions.We also consider the case that every cyclic rotation of the cycle form of the permutation avoids a pattern of length 4 and enumerate two such cases.