Journal of Combinatorics

Volume 6 (2015)

Number 1–2

Two examples of unbalanced Wilf-equivalence

Pages: 55 – 67



Alexander Burstein (Department of Mathematics, Howard University, Washington, D.C., U.S.A.)

Jay Pantone (Department of Mathematics, University of Florida, Gainesville, Fl., U.S.A.)


We prove that the set of patterns {1324, 3416725} is Wilf-equivalent to the pattern 1234 and that the set of patterns {2143, 3142, 246135} is Wilf-equivalent to the set of patterns {2413, 3142}. These are the first known unbalanced Wilf-equivalences for classical patterns between finite sets of patterns.


permutation patterns, unbalanced Wilf-equivalence

2010 Mathematics Subject Classification

Primary 05A05. Secondary 05A15.

Published 20 March 2015