Restricted 123-avoiding Baxter permutations and the Padovan numbers

Abstract

Baxter studied a particular class of permutations by considering fixed points of the composite of commuting functions. This class is called Baxter permutations. In this paper we investigate the number of 123-avoiding Baxter permutations of length $n$ that also avoid (or contain a prescribed number of occurrences of) another certain pattern of length $k$. In several interesting cases the generating function depends only on $k$ and is expressed via the generating function for the Padovan numbers.