Generating permutations with restricted containers

被引：16

作者：

Albert, Michael H. ^{[1
]}

Homberger, Cheyne ^{[2
]}

Pantone, Jay ^{[3
]}

Shar, Nathaniel ^{[4
]}

Vatter, Vincent ^{[5
]}

机构：

[1] Univ Otago, Dept Comp Sci, Dunedin, New Zealand

[2] Univ Maryland Baltimore Cty, Dept Math, Baltimore, MD 21228 USA

[3] Dartmouth Coll, Dept Math, Hanover, NH 03755 USA

[4] Rutgers State Univ, Dept Math, New Brunswick, NJ USA

[5] Univ Florida, Dept Math, Gainesville, FL 32611 USA

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2018年 / 157卷

基金：

美国国家科学基金会;

关键词：

Permutation patterns; Enumeration; Stack; Sorting machine; GENERALIZED SCHRODER NUMBER; FORBIDDEN SUBSEQUENCES; 1324-AVOIDING PERMUTATIONS; ENUMERATION; SERIES; EQUATIONS; PATTERNS; TREES;

D O I：

10.1016/j.jcta.2018.02.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate a generalization of stacks that we call C-machines. We show how this viewpoint rapidly leads to functional equations for the classes of permutations that C-machines generate, and how these systems of functional equations can be iterated and sometimes solved. General results about the rationality, algebraicity, and the existence of Wilfian formulas for some classes generated by C-machines are given. We also draw attention to some relatively small permutation classes which, although we can generate thousands of terms of their counting sequences, seem to not have D-finite generating functions. (C) 2018 Elsevier Inc. All rights reserved.

引用

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页码：205 / 232

页数：28

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