| Permutation classes arise naturally in many disparate fields, ranging from the analysis of sorting machines to the study of Schubert varieties. We characterize the finitely based permutation classes with finitely labeled generating trees, and describe how to systematically enumerate these classes. We then extend Zeilberger's enumeration schemes, which provide another powerful technique for the systematic enumeration of permutation classes. Finally, we study grid classes, characterize the permutation classes that lie in a grid class, and use this to derive a new proof of the Fibonacci dichotomy for permutation classes. |
