A New Class of Wilf-Equivalent Permutations

Authors:
Zvezdelina Stankova;Julian West
Affiliations:
Department of Mathematics and Computer Science, Mills College, Oakland, CA, USA. stankova@mills.edu;Department of Mathematics and Statistics, University of Victoria, Canada. westj@mala.bc.ca/ julian@math.uvic.ca
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2002

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Abstract

For about 10 years, the classification up to Wilf equivalence of permutation patterns was thought completed up to length 6. In this paper, we establish a new class of Wilf-equivalent permutation patterns, namely, (in − 1, in − 2, in, τ) ∼ (in − 2, in, in − 1, τ) for any τ∈iSn−3. In particular, at level in = 6, this result includes the only missing equivalence (546213) ∼ (465213), and for in = 7 it completes the classification of permutation patterns by settling all remaining cases in iS7.