Permutations sortable by two stacks in parallel and quarter plane walks
نویسندگان
چکیده
منابع مشابه
Permutations sortable by two stacks in parallel and quarter plane walks
At the end of the 1960s, Knuth characterised in terms of forbidden patterns the permutations that can be sorted using a stack. He also showed that they are in bijection with Dyck paths and thus counted by the Catalan numbers. Subsequently, Pratt and Tarjan asked about permutations that can be sorted using two stacks in parallel. This question is significantly harder, and the associated counting...
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In his seminal work The Art of Computer Programming [2], Knuth was the first to consider a number of classic data structures from the point of view of the permutations they could produce from the identity permutation, or equinumerously, the permutations which the data structure can sort. Famously, he noticed that the permutations obtainable using a single stack are exactly those which avoid the...
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We address the problem of the number of permutations that can be sorted by two stacks in series. We do this by first counting all such permutations of length less than 20 exactly, then using a numerical technique to obtain nineteen further coefficients approximately. Analysing these coefficients by a variety of methods we conclude that the OGF behaves as S(z) ∼ A(1− μ · z) , where μ = 12.45± 0....
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2015
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2014.08.024