Enumeration of cyclic permutations in vector grid classes
Combinatorics
2018-08-27 v2
Abstract
A grid class consists of permutations whose pictorial depiction can be partitioned into increasing and decreasing parts as determined by a given matrix. In this paper, we introduce a method for enumerating cyclic permutations in vector grid classes by establishing a bijective relationship with certain necklaces. We use this method to complete the enumeration of cyclic permutations in the length 3 vector grid classes. In addition, we define an analog of Wilf-equivalence between these sets. We conclude by discussing cyclic permutations in alternating grid classes.
Cite
@article{arxiv.1606.04502,
title = {Enumeration of cyclic permutations in vector grid classes},
author = {Kassie Archer and L. -K. Lauderdale},
journal= {arXiv preprint arXiv:1606.04502},
year = {2018}
}