Postprint version. Published in Journal of Combinatorial Theory, Series A, Volume 59, Issue 1, January 1, 1992, pages 111-124.
The definitive version is available at https://doi.org/10.1016/0097-3165(92)90102-Z.
Based on the binary tree decomposition of a permutation, a natural vector space of permutation statistics is defined. Besides containing many well known permutation statistics, this space provides the general context for an archetypal recurrence relationship that contains most of the classic combinatorial sequences and some of their known generalizations.