Subregularity in infinitely labeled generating trees of restricted permutations

In this paper, we revisit the application of generating trees to the pattern avoidance problem for permutations. In particu-lar, we study this problem for certain general sets of patterns and propose a new procedure leveraging the FinLabel al-gorithm and exploiting the subregularities in the associated generating trees. We consider some general kinds of generat-ing trees for which the FinLabel algorithm fails to determine in a finite number of iterations the generating function that enumerates the underlying class of permutations. Our proce-dure provides a unified approach in these cases leading to a system of equations satisfied by a certain finite set of gener-ating functions which can be readily solved with the aid of programming.(c) 2022 Elsevier Inc. All rights reserved.