[2] A principal permutation class is a class whose basis consists of only a single permutation.
Thus, for instance, the stack-sortable permutations form a principal permutation class, defined by the forbidden pattern 231.
In the late 1980s, Richard Stanley and Herbert Wilf conjectured that for every proper permutation class
permutations in the class is upper bounded by
This was known as the Stanley–Wilf conjecture until it was proved by Adam Marcus and Gábor Tardos.
[3] However although the limit (a tight bound on the base of the exponential growth rate) exists for all principal permutation classes, it is open whether it exists for all other permutation classes.
[4] Two permutation classes are called Wilf equivalent if, for every
The counting functions and Wilf equivalences among many specific permutation classes are known.