The enumeration of permutations sortable by pop stacks in parallel

Smith, Rebecca; Vatter, Vincent

doi:10.1016/j.ipl.2009.02.014

Cited by 6 publications

(7 citation statements)

References 5 publications

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“…In Figure 7 we see the permutation 64321587(12)(10)9(14)(13) (11). In this case b 1 = 5, b 2 = 1, b 3 = 2, b 4 = 3, and b 5 = 3.…”

Section: Theorem 5 (Aleksandrowicz Asinowski and Barequet) The Classi...mentioning

confidence: 98%

“…Both Avis and Newborn [5] and Atkinson and Stitt [4] studied pop stacks in series. Atkinson and Sack [3] and Smith and Vatter [11] also considered pop stacks in parallel. It follows from the work of Avis and Newborn that a permutation π is sortable by one pass through a pop stack if and only if π avoids 231 and 312.…”

Section: Sorting Networkmentioning

confidence: 99%

“…Then, we wrap the resulting strip of separated rectangles around the twisted cylinder of width 3. The two-pop-stack sortable permutation 64321587(12)(10)9(14)(13) (11) and its corresponding polyomino…”

Section: Theorem 5 (Aleksandrowicz Asinowski and Barequet) The Classi...mentioning

confidence: 99%

“…Figure 7:The two-pop-stack sortable permutation 64321587(12)(10)9(14)(13)(11) and its corresponding polyomino…”

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confidence: 99%

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Two-stack-sorting with pop stacks

Pudwell,

Smith

2018

Preprint

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We consider the set of permutations that are sorted after two passes through a pop stack. We characterize these permutations in terms of forbidden patterns (classical and barred) and enumerate them according to the ascent statistic. Then we show these permutations to be in bijection with a special family of polyominoes. As a consequence, the permutations sortable by this machine are shown to have the same enumeration as three classical permutation classes.

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“…In Figure 7 we see the permutation 64321587(12)(10)9(14)(13) (11). In this case b 1 = 5, b 2 = 1, b 3 = 2, b 4 = 3, and b 5 = 3.…”

Section: Theorem 5 (Aleksandrowicz Asinowski and Barequet) The Classi...mentioning

confidence: 98%

Section: Sorting Networkmentioning

confidence: 99%

Section: Theorem 5 (Aleksandrowicz Asinowski and Barequet) The Classi...mentioning

confidence: 99%

“…Figure 7:The two-pop-stack sortable permutation 64321587(12)(10)9(14)(13)(11) and its corresponding polyomino…”

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confidence: 99%

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Two-stack-sorting with pop stacks

Pudwell,

Smith

2018

Preprint

Self Cite

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“…Knuth characterised the set of permutations that can be sorted by a single pass through an infinite stack as the set of permutations that avoid 231 [11]. Since then many variants of the problem have been studied, for example [1,2,3,4,5,6,7,8,9,13,14,15,16,17,18]. The set of permutations sortable by a stack of depth 2 and an infinite stack in series has a basis of 20 permutations [7], while for two infinite stacks in series there is no finite basis [12].…”

Section: Introductionmentioning

confidence: 99%

Permutations Sorted by a Finite and an Infinite Stack in Series

Elder

Goh

2018

Language and Automata Theory and Applications

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Enumerating permutations sortable by k passes through a pop-stack

Claesson

Guðmundsson

2019

Advances in Applied Mathematics

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In an exercise in the first volume of his famous series of books, Knuth considered sorting permutations by passing them through a stack. Many variations of this exercise have since been considered, including allowing multiple passes through the stack and using different data structures. We are concerned with a variation using pop-stacks that was introduced by Avis and Newborn in 1981. Let P k (x) be the generating function for the permutations sortable by k passes through a pop-stack. The generating function P 2 (x) was recently given by Pudwell and Smith (the case k = 1 being trivial). We show that P k (x) is rational for any k. Moreover, we give an algorithm to derive P k (x), and using it we determine the generating functions P k (x) for k ≤ 6.

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The enumeration of permutations sortable by pop stacks in parallel

Cited by 6 publications

References 5 publications

Two-stack-sorting with pop stacks

Two-stack-sorting with pop stacks

Permutations Sorted by a Finite and an Infinite Stack in Series

Enumerating permutations sortable by k passes through a pop-stack

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