Year: 2002
Type: preprint
Abstract: Circular permutations on {1,2,...,n} that avoid a given pattern correspond to ordinary (linear) permutations that end with n and avoid all cyclic rotations of the pattern. Three letter patterns are all but unavoidable in circular permutations and here we give explicit formulas for the number of circular permutations that avoid one four letter pattern. In the three essentially distinct cases, the counts are as follows: the Fibonacci number F_{2n-3} for the pattern 1324, 2^{n-1}-(n-1) for 1342, and 2^{n}+1-2n-{n}choose{3} for 1234.
Source: arXiv (Cornell University)
Author: Callan, David
Institution: University of Wisconsin–Madison
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1513484977