Journal of Combinatorics

Volume 11 (2020)

Number 1

Enumeration of cyclic permutations in vector grid classes

Pages: 203 – 230



Kassie Archer (Department of Mathematics, University of Texas,Tyler, Tx., U.S.A.)

L.-K. Lauderdale (Department of Mathematics, Towson University, Towson, Maryland, U.S.A.)


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 Wilfe-quivalence between these sets. We conclude by discussing cyclic permutations in alternating grid classes.

Received 1 September 2016

Published 27 September 2019