On permutation pattern classes with two restrictions only
نویسنده
چکیده
Permutation pattern classes that are defined by avoiding two permutations only and which contain only finitely many simple permutations are characterized and their growth rates are determined.
منابع مشابه
Compositions of pattern restricted sets of permutations
The composition of two pattern restricted classes X,Y is the set of all permutation products θφ where θ ∈ X,φ ∈ Y . This set is also defined by pattern restrictions. Examples are given where this set of restrictions is finite and where it is infinite. The composition operation is studied in terms of machines that sort and generate permutations. The theory is then applied to a multistage sorting...
متن کاملWreath Products of Permutation Classes
A permutation class which is closed under pattern involvement may be described in terms of its basis. The wreath product construction X o Y of two permutation classes X and Y is also closed, and we investigate classes Y with the property that, for any finitely based class X, the wreath product X o Y is also finitely based.
متن کاملMILP models and valid inequalities for the two-machine permutation flowshop scheduling problem with minimal time lags
In this paper, we consider the problem of scheduling on two-machine permutation flowshop with minimal time lags between consecutive operations of each job. The aim is to find a feasible schedule that minimizes the total tardiness. This problem is known to be NP-hard in the strong sense. We propose two mixed-integer linear programming (MILP) models and two types of valid inequalities which aim t...
متن کاملPattern Classes of Permutations
Though still a relatively young subject within discrete mathematics, the study of pattern classes of permutations is one of the fastest growing and is useful in theoretical computer science as well as various areas of mathematics. There are two commonly used forms of notation for permutations: a1a2 . . . an denotes the permutation which sends i to ai for i = 1, 2, . . . , n, where each ai repre...
متن کاملMesh Patterns and the Expansion of Permutation Statistics as Sums of Permutation Patterns
Any permutation statistic f : S → C may be represented uniquely as a, possibly infinite, linear combination of (classical) permutation patterns: f = Στλf (τ)τ . To provide explicit expansions for certain statistics, we introduce a new type of permutation patterns that we call mesh patterns. Intuitively, an occurrence of the mesh pattern p = (π,R) is an occurrence of the permutation pattern π wi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007