Michael H. Albert
Published 2002-12-11, updated 2015-08-05Version 2
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.
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)
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