Enumerations of specific permutation classes

A more efficient algorithm using functional equations was given by Johansson & Nakamura (2014), which was enhanced by Conway & Guttmann (2015), and then further enhanced by Conway, Guttmann & Zinn-Justin (2018) who give the first 50 terms of the enumeration.

Bevan et al. (2017) have provided lower and upper bounds for the growth of this class.

Only 3 of these remain unenumerated, and their generating functions are conjectured not to satisfy any algebraic differential equation (ADE) by Albert et al. (2018); in particular, their conjecture would imply that these generating functions are not D-finite.

To create each heatmap, one million permutations of length 300 were sampled uniformly at random from the class.

Higher resolution versions can be obtained at PermPal 4321, 4123 4321, 3412 4123, 3214 4123, 2143 4312, 3421 4213, 2431 4231, 3412 4231, 3142 4213, 3241 4213, 3124 4213, 2314 4213, 3412 4123, 3142 4321, 4312 4312, 4231 4312, 4213 4312, 3412 4231, 4213 4213, 4132 4213, 4123 4213, 2413 4213, 3214 3142, 2413 The Database of Permutation Pattern Avoidance, maintained by Bridget Tenner, contains details of the enumeration of many other permutation classes with relatively few basis elements.