Enumeration of several two-by-four classes

Abstract

We use catalytic variables to derive generating functions for the permutation classes $Av(\text{4123},\text{1324})$, $Av(\text{4123},\text{1243})$, and $Av(\text{4123},\text{1342})$. Each generating function is algebraic of degree two, and the growth rates of the classes are 4, 5, and $\alpha$, respectively, where $\alpha \approx 4.17035$. As a consequence of our analysis, we see that a typical large permutation in $Av(\text{4123},\text{1324})$ is likely to also avoid $\text{3124}$, and is even more likely to avoid $\text{31524}$. Large permutations which avoid $\text{4123}$ and $\text{1243}$ are likely to also avoid $\text{1423}$.

22 pages

References in corpus (1)

• Central binomial coefficients also count (2431,4231,1432,4132)-avoiders

Cited by in corpus (1)

• Juxtaposing Catalan permutation classes with monotone ones