Pattern avoiding permutations are context - sensitive Murray Elder
نویسنده
چکیده
We prove that a variant of the insertion encoding of Albert, Linton and Ruškuc for any class of pattern avoiding permutations is context-senstive. It follows that every finitely based class of permutations bijects to a context-sensitive language.
منابع مشابه
Pattern Avoiding Permutations
We establish a bijection from the set of all permutations (of a given length) that avoid a pattern q and a context-sensitive language.
متن کاملPattern Avoiding Permutations Are Context-sensitive
We establish a bijection from the set of all permutations (of a given length) that avoid a pattern q and a context-sensitive language.
متن کاملRecounted by Murray Elder and Vince Vatter
A permutation is an arrangement of a finite number of distinct elements of a linear order, for example, e, π, 0, √ 2 and 3412. Two permutations are order isomorphic if the have the same relative ordering. We say a permutation τ contains or involves a permutation β if deleting some of the entries of π gives a permutation that is order isomorphic to β, and we write β ≤ τ . For example, 534162 (wh...
متن کاملPermutations of context-free, ET0L and indexed languages
For a language L, we consider its cyclic closure, and more generally the language C(L), which consists of all words obtained by partitioning words from L into k factors and permuting them. We prove that the classes of ET0L and EDT0L languages are closed under the operators C. This both sharpens and generalises Brandstädt’s result that if L is context-free then C(L) is context-sensitive and not ...
متن کاملPermutations Generated by a Depth 2 Stack and an Infinite Stack in Series are Algebraic
We prove that the class of permutations generated by passing an ordered sequence 12 . . . n through a stack of depth 2 and an infinite stack in series is in bijection with an unambiguous context-free language, where a permutation of length n is encoded by a string of length 3n. It follows that the sequence counting the number of permutations of each length has an algebraic generating function. ...
متن کامل