Generalized pattern avoidance

Abstract

The notion of classical pattern avoidance is extended by defining a new kind of generalized pattern avoidance, and the invariance of generalized restricted permutations on the algebraic operation Γ is proved. Furthermore, one kind of the generalized pattern avoidance, that is, the pattern 231 is discussed. The classifications and combinatorial calculations for generalized 231 restricted permutations are given. At last, a conjecture is presented. The new generalized patterns avoidance may promote the research on restricted permutations.