Some simple varieties of trees arising in permutation analysis

Abstract

After extending classical results on simple varieties of trees to trees counted by their number of leaves, we describe a filtration of the set of permutations based on their strong interval trees. For each subclass we provide asymptotic formulas for number of trees (by leaves), average number of nodes of fixed arity, average subtree size sum, and average number of internal nodes. The filtration is motivated by genome comparison of related species.

Keywords

• permutations
• simple varieties of trees
• random generation
• tree parameters
• asymptotic formulas
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]