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arXiv · 1606.04502

Enumeration of cyclic permutations in vector grid classes

Kassie Archer·L. -K. Lauderdale
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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.

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Kassie Archer, L. -K. Lauderdale. 2018-08-23. Enumeration of cyclic permutations in vector grid classes. https://arxiv.org/abs/1606.04502

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