We give an explicit formula for the number of permutations that cyclically avoid 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 οn is given by n! times the convergent series Σ∞k=-∞ (3/2φ(k+1/3)n for n ≤ 2.
|Number of pages||6|
|Journal||SIAM Journal on Discrete Mathematics|
|State||Published - 2016|
Bibliographical notePublisher Copyright:
Copyright © by SIAM.
- Cyclic consecutive pattern avoidance
- Integral operators
- Trace class operators
ASJC Scopus subject areas
- Mathematics (all)