Cyclic and lift closures for k...21-avoiding permutations

Jean-Luc Baril (1)

1 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]

We prove that the cyclic closure of the permutation class avoiding the pattern is finitely based. The minimal length of a minimal permutation is and these basis permutations are enumerated by where is the th Catalan number. We also define lift operations and give similar results. Finally, we consider the toric closure of a class and we propose some open problems.

Mots clés: Pattern avoiding permutation class; Cyclic; lift and toric closures

Domaines: Combinatoire [math.CO]

Jean-Luc Baril. Cyclic and lift closures for k...21-avoiding permutations. Discrete Mathematics, 2011, 311 (1), pp.51-57. ⟨10.1016/j.disc.2010.09.021⟩. ⟨hal-00785284⟩