避免 321 的排列的精细结构
组合数学
2015-08-07 v2
摘要
我们确定了各类不含长度为三或更长的递减序列的排列类的双变量生成函数。引入了排列的绝对不可分解性概念,并用于枚举具有避免321的块结构且各块亦具有此种结构(递归地)的排列。讨论了这些结果的推广。
引用
@article{arxiv.math/0212163,
title = {The fine structure of 321 avoiding permutations},
author = {Michael H. Albert},
journal= {arXiv preprint arXiv:math/0212163},
year = {2015}
}
备注
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)