Two operads are said to belong to the same Wilf class if they have the same generating series. We discuss possible Wilf classifications of non-symmetric operads with monomial relations. As a corollary, this would give the same classification for the operads with a finite Groebner basis. Generally, there is no algorithm to decide whether two finitely presented operads belong to the same Wilf class. Still, we show that if an operad has a finite Groebner basis, then the monomial basis of the operad forms an unambiguous context-free language. Moreover, we discuss the deterministic grammar which defines the language. The generating series of the operad can be obtained as a result of an algorithmic elimination of variables from the algebraic system of equations defined by the Chomsky--Schutzenberger enumeration theorem. We then focus on the case of binary operads with a single relation. The approach is based on the results by Rowland on pattern avoidance in binary trees. We improve and refine Rowland's calculations and empirically confirm his conjecture. Here we use both the algebraic elimination and the direct calculation of formal power series from algebraic systems of equations. Finally, we discuss the connection of Wilf classes with algorithms for the Quillen homology of operads calculation.

翻译：两种剧本据说属于相同的威尔夫类。 我们讨论威尔夫类中可能的非对称剧本的分类, 与单一关系。 作为必然结果, 这将给剧本中有限的格鲁布纳类中的变量提供相同的分类。 一般来说, 没有算法来决定两种有限展示的剧本是否属于同一威尔夫类。 但是, 我们显示, 如果剧本有有限的格鲁布纳基础, 那么歌本的单一基础将形成一种明确的无背景语言 。 此外, 我们讨论定义语言的确定性语法。 剧本系列的生成可以作为消除Chomsky- Schutzenberger 计数等式中定义的等式变数的算法系统的结果 。 我们随后关注的是具有单一关系的二进制剧本级的剧本级剧本。 我们改进并改进了罗兰的计算方法, 并用实验性的方式确认了其定義语法序列的等式变数 。 我们最后使用Chosky- Schengial 计算法的直成型变数系统 。