The enumeration of three pattern classes
نویسندگان
چکیده
The structure of three pattern classes Av(2143, 4321), Av(2143, 4312) and Av(1324, 4312) is determined using the machinery of monotone grid classes. This allows the permutations in these classes to be described in terms of simple diagrams and regular languages and, using this, the rational generating functions which enumerate these classes are determined.
منابع مشابه
Enumeration Schemes for Words Avoiding Permutations
The enumeration of permutation classes has been accomplished with a variety of techniques. One wide-reaching method is that of enumeration schemes, introduced by Zeilberger and extended by Vatter. In this paper we further extend the method of enumeration schemes to words avoiding permutation patterns. The process of finding enumeration schemes is programmable and allows for the automatic enumer...
متن کاملThe Enumeration of Three Pattern Classes using Monotone Grid Classes
The structure of the three pattern classes defined by the sets of forbidden permutations {2143, 4321}, {2143, 4312} and {1324, 4312} is determined using the machinery of monotone grid classes. This allows the permutations in these classes to be described in terms of simple diagrams and regular languages and, using this, the rational generating functions which enumerate these classes are determi...
متن کاملEnumeration of Some Classes of Words Avoiding Two Generalized Patterns of Length Three
The method we have applied in [BFP] to count pattern avoiding permutations is adapted to words. As an application, we enumerate several classes of words simultaneously avoiding two generalized patterns of length 3.
متن کاملEnumeration Schemes for Restricted Permutations
Zeilberger’s enumeration schemes can be used to completely automate the enumeration of many permutation classes. We extend his enumeration schemes so that they apply to many more permutation classes and describe the Maple package WilfPlus, which implements this process. We also compare enumeration schemes to three other systematic enumeration techniques: generating trees, substitution decomposi...
متن کاملEnumeration formulæ for pattern restricted Stirling permutations
We classify k-Stirling permutations avoiding a set of ordered patterns of length three according to Wilf-equivalence. Moreover, we derive enumeration formulæ for all of the classes using a variety of techniques such as the kernel method, a bijection related to a classical result of Simion and Schmidt, and also structural decompositions of k-Stirling permutations via the so-called block decompos...
متن کامل