Permutations Generated by a Stack of Depth 2 and an Infinite Stack in Series
نویسندگان
چکیده
منابع مشابه
Permutations Generated by a Stack of Depth 2 and an Infinite Stack in Series
We prove that the set of permutations generated by a stack of depth two and an infinite stack in series has a basis (defining set of forbidden patterns) consisting of 20 permutations of length 5, 6, 7 and 8. We prove this via a “canonical” generating algorithm.
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 کاملPermutations Generated by a Depth 2 and 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. ...
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In the 60’s, Knuth introduced stack-sorting and serial compositions of stacks. In particular, one significant question arise out of the work of Knuth: how to decide efficiently if a given permutation is sortable with 2 stacks in series? Whether this problem is polynomial or NP-complete is still unanswered yet. In this article we introduce 2-stack pushall permutations which form a subclass of 2-...
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We study sorting machines consisting of a stack and a pop stack in series, with or without a queue between them. While there are, a priori, four such machines, only two are essentially different: a pop stack followed directly by a stack, and a pop stack followed by a queue and then by a stack. In the former case, we obtain complete answers for the basis and enumeration of the sortable permutati...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2006
ISSN: 1077-8926
DOI: 10.37236/1094