Year: 2013
Type: preprint
Abstract: We give an explicit formula for the number of permutations avoiding cyclically a consecutive pattern in terms of the spectrum of the associated operator of the consecutive pattern. As an example, the number of cyclically consecutive $123$-avoiding permutations in ${\mathfrak S}_{n}$ is given by $n!$ times the convergent series ${\displaystyle \sum_{k=-\infty}^{\infty} \left(\frac{\sqrt{3}}{2π(k+1/3)}\right)^{n}}$ for $n \geq 2$.
Source: arXiv (Cornell University)
Author: Ehrenborg, Richard
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Security Agency
Awards: G474822827, G7845798442
OpenAlex ID: W2949612300