The fine structure of 321 avoiding permutations
Abstract
Bivariate generating functions for various subsets of the class of permutations containing no descending sequence of length three or more are determined. The notion of absolute indecomposability of a permutation is introduced, and used in enumerating permutations which have a block structure avoiding 321 and whose blocks also have such structure (recursively). Generalizations of these results are discussed.
Cite
@article{arxiv.math/0212163,
title = {The fine structure of 321 avoiding permutations},
author = {Michael H. Albert},
journal= {arXiv preprint arXiv:math/0212163},
year = {2015}
}
Comments
18 pages, 4 figures. Corrected mistake in conjectured basis of the substitution closure of Av(321) (thanks to William Kuszmaul for pointing this out). That conjecture has been confirmed (M.D. Atkinson, N. Ruskuc, R. Smith, Substitution-closed patterns classes, J. Combinat Theory A 118 (2011), 317-340. DOI: 10.1016/j.jcta.2010.10.006, see table 1, page 339)