ON THE GROWTH OF MERGES AND STAIRCASES OF PERMUTATION CLASSES

被引：5

作者：

Albert, Michael ^{[1
]}

Pantone, Jay ^{[2
]}

Vatter, Vincent ^{[3
]}

机构：

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

[2] Marquette Univ, Dept Math Stat & Comp Sci, Milwaukee, WI 53233 USA

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

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2019年 / 49卷 / 02期

关键词：

Permutation patterns; exponential growth rate; staircase classes; LIMIT;

D O I：

10.1216/RMJ-2019-49-2-355

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

There is a well-known upper bound due to Claesson, Jelinek and Steingrimsson [13] for the growth rate of the merge of two permutation classes. Curiously, there is no known merge for which this bound is not achieved. Using linear algebraic techniques and appealing to the theory of Toeplitz matrices, we provide sufficient conditions for the growth rate to equal this upper bound. In particular, our results apply to all merges of principal permutation classes. We end by demonstrating how our techniques relate to the results of Bona [9, 10].

引用

页码：355 / 367

页数：13

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