Consecutive patterns in circular permutations
Combinatorics
2021-07-13 v1
Abstract
In their study of cyclic pattern containment, Domagalski et al. conjecture differential equations for the generating functions of circular permutations avoiding consecutive patterns of length 3. In this note, we prove and significantly generalize these conjectures. We show that, for every consecutive pattern beginning with 1, the bivariate generating function counting occurrences of in circular permutations can be obtained from the generating function counting occurrences of in (linear) permutations. This includes all the patterns for which the latter generating function is known.
Cite
@article{arxiv.2107.04717,
title = {Consecutive patterns in circular permutations},
author = {Sergi Elizalde and Bruce Sagan},
journal= {arXiv preprint arXiv:2107.04717},
year = {2021}
}