NBB Bases of Some Lattices of Pattern-Avoiding Permutations

Abstract

In this paper, we will determine the NBB bases with respect to a certain standard ordering of atoms of lattices of \(321\)-\(312\)-\(231\)-avoiding permutations and of \(321\)-avoiding permutations with the weak Bruhat order. Using our expressions of NBB bases, we will calculate the Möbius numbers of these lattices. These values are shown to be related to Fibonacci polynomials.