Classical Sequences Revisited with Permutations Avoiding Dotted Pattern

Abstract

Inspired by the definition of the barred pattern-avoiding permutation, we introduce the new concept of dotted pattern for permutations. We investigate permutations classes avoiding dotted patterns of length at most 3, possibly along with other classical patterns. We deduce some enumerating results which allow us to exhibit new families of permutations counted by the classical sequences: $2^{n}$, Catalan, Motzkin, Pell, Fibonacci, Fine, Riordan, Padovan, Eulerian.