Enumeration of cyclic permutations in vector grid classes

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.

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Received 1 September 2016

Published 27 September 2019