Packing Densities of Patterns

Abstract

The packing density of a permutation $\pi$ of length $n$ is the maximum proportion of subsequences of length $n$ which are order-isomorphic to $\pi$ in arbitrarily long permutations $\sigma$. For the generalization to patterns $\pi$ which may have repeated letters, two notions of packing density have been defined. In this paper, we show that these two definitions are equivalent, and we compute the packing density for new classes of patterns.