A binary tree decomposition space of permutation statistics (Q1185886)

This paper is written to propose a possible framework for a systematic study of permutation statistics which have arisen in connection with numerous applications of combinatorics to a wide spectrum of mathematics. The approach used here is to introduce a natural vector space of permutation statistics based on the binary tree decomposition of a permutation. The space introduced contains many well-known permutation statistics, and also provides the setting for an archetypal recurrence relationship which contains many classical combinatorial sequences.