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Stack sortable permutations

1981
*
Discrete Mathematics
*

The class SS, of

doi:10.1016/0012-365x(81)90165-5
fatcat:4537o6knh5antizizaanulltl4
*stack**sortable**permutations*is known to be in l-l correspondence with the set of n-noded binary trees. ... We use this corresponden(-e to show that many properties of a binary tree are related to different types of monotonic subsequences in the corresponding*permutation*. ... We denote by SS, the class of*permutations*of order n which are*sortable*with a*stack*. and by SR, the class of*permutations*of the same order which are reraizabie with a*stack*. ...##
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Counting 3-Stack-Sortable Permutations
[article]

2020
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arXiv
*
pre-print

The same method yields a recurrence relation for W_3(n), the number of 3-

arXiv:1903.09138v3
fatcat:kjfanablv5byhlk7ltqxkf7c7e
*stack*-*sortable**permutations*in S_n. ... As a first application, we give a new proof of Zeilberger's formula for the number of 2-*stack*-*sortable**permutations*in S_n. ... In this section, we count 3-*stack*-*sortable**permutations*by viewing them as preimages of 2-*stack*-*sortable**permutations*. ...##
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Stack words and a bound for 3-stack sortable permutations
[article]

2020
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arXiv
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pre-print

We use

arXiv:1903.04113v4
fatcat:dtdbwteeyjgydlrchrrayho7ia
*stack*words to find a new, simple proof for the best known upper bound for the number of 3-*stack**sortable**permutations*of a given length. ... This is the first time that*stack*words are used to obtain such a result. ... Enumerating t-*stack**sortable**permutations*for t > 1 is extremely difficult. Let W t (n) be the number of t-*stack**sortable**permutations*of length n. ...##
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Describing West-3-stack-sortable permutations with permutation patterns
[article]

2012
*
arXiv
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pre-print

We use this method to describe West-3-

arXiv:1110.1219v3
fatcat:mgr2gwkstvblnd6kttc3dhdfau
*stack*-*sortable**permutations*, that is,*permutations*that are sorted by three passes through a*stack*. ... We describe a new method for finding patterns in*permutations*that produce a given pattern after the*permutation*has been passed once through a*stack*. ... The author would like to thank Anders Claesson for suggesting the problem of describing West-3-*stack*-*sortable**permutations*, as well as for help with testing Theorem 4.6 with a computer. ...##
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Asymptotics of 3-stack-sortable permutations
[article]

2020
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arXiv
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pre-print

We derive a simple functional equation with two catalytic variables characterising the generating function of 3-

arXiv:2009.10439v3
fatcat:7ugl6tjmuzcuvdirwkdoudgomm
*stack*-*sortable**permutations*. ... Let W k (n) be the set of k-*stack*-*sortable**permutations*in S n . ... Introduction A*permutation*is said to be*stack*-*sortable*if, when it is passed through a*stack*, the result is the increasing*permutation*. We describe the*stack*-sorting map below. ...##
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2-stack pushall sortable permutations
[article]

2013
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arXiv
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pre-print

In this article we introduce 2-

arXiv:1303.4376v1
fatcat:rwyz4vlud5f73ifmsbh3vwpyyu
*stack*pushall*permutations*which form a subclass of 2-*stack**sortable**permutations*and show that these two classes are closely related. ... Moreover, we give an optimal O(n^2) algorithm to decide if a given*permutation*of size n is 2-*stack*pushall*sortable*and describe all its sortings. ... Hence π (i) is 2-*stack*pushall*sortable*. 2-*stack**sortable**permutations*form a*permutation*class, so that π (k) must be 2-*stack**sortable*. ...##
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Generalizations of two-stack-sortable permutations
[article]

2002
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arXiv
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pre-print

In this thesis, we apply the

arXiv:math/0209313v2
fatcat:vfpe74rvgrb5pd56pv753qkdy4
*stack*sorting operator to r-*permutations*and construct the functional equation for the generating function of two-*stack*-*sortable*k-tuple r-*permutations*counted by descents ... We solve the functional equation and give explicit formulas for the number of two-*stack*-*sortable*r-*permutations*. ... TWO-*STACK*-*SORTABLE*r-*PERMUTATIONS*. TWO-*STACK*-*SORTABLE*r-*PERMUTATIONS*. TWO-*STACK*-*SORTABLE*r-*PERMUTATIONS*. TWO-*STACK*-*SORTABLE*r-*PERMUTATIONS*. PARALLEL RESULTS . ...##
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Fighting fish and two-stack sortable permutations
[article]

2019
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arXiv
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pre-print

In this article, we explore the bijective aspect of fighting fish by establishing a bijection to two-

arXiv:1711.05713v2
fatcat:mwvmog7prbcjblshvxa2rrmyoy
*stack**sortable**permutations*, using a new recursive decomposition of these*permutations*. ...*sortable**permutations*and non-separable planar maps. ... Given a two-*stack**sortable**permutation*π, let S(π) be the result of sorting π once through a*stack*. ...##
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Permutations sortable by two stacks in series
[article]

2016
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arXiv
*
pre-print

We address the problem of the number of

arXiv:1510.08663v2
fatcat:xvh4gk36szhohi2ubhphzzxmcy
*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. ... Unfortunately, both these cases correspond to an exponentially small subset of the full set of*stack*-*sortable**permutations*. ...##
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Asymptotics of 3-Stack-Sortable Permutations

2021
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Electronic Journal of Combinatorics
*

We derive a simple functional equation with two catalytic variables characterising the generating function of 3-

doi:10.37236/10134
fatcat:hi2merl62bgb7fzcxsfoj6juce
*stack*-*sortable**permutations*. ... Let W k (n) be the set of k-*stack*-*sortable**permutations*in S n . ... A*permutation*is called k-*stack*-*sortable*if iteratively applying the*stack*-sorting map to it k times results in the increasing*permutation*. ...##
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k-pop stack sortable permutations and 2-avoidance
[article]

2019
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arXiv
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pre-print

We consider

arXiv:1911.03104v2
fatcat:hxryzkvdx5ft7eaytiyphm35j4
*permutations**sortable*by k passes through a deterministic pop*stack*. ... Our characterisation demands a more precise definition than in previous literature of what it means for a*permutation*to avoid a set of barred and unbarred patterns. ... Recall that by Thm. 3.4] and Marcus-Tardos [8] the function counting the number of*permutations*of length n in any Av(F ) for F non-empty is either polynomial or exponential. ...##
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Permutations sortable by two stacks in parallel and quarter plane walks
[article]

2014
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arXiv
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pre-print

In particular, a

arXiv:1312.4487v3
fatcat:jdrroduskbh67hpbrid5fpd6jm
*sortable**permutation*can now be sorted by several distinct sequences of*stack*operations. Moreover, in order to be*sortable*, a*permutation*must avoid infinitely many patterns. ... At the end of the 1960s, Knuth characterised the*permutations*that can be sorted using a*stack*in terms of forbidden patterns. ... Denton [11] has presented an algorithm for this problem whose complexity is O(n 5 2 n ) (for enumerating the*sortable**permutations*of length n). ...##
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Permutations sortable by n-4 passes through a stack
[article]

2009
*
arXiv
*
pre-print

We characterise and enumerate

arXiv:0812.0143v2
fatcat:bb56laecqra67oc2bxvv42lk7i
*permutations*that are*sortable*by n-4 passes through a*stack*. ... We conjecture the number of*permutations**sortable*by n-5 passes, and also the form of a formula for the general case n-k, which involves a polynomial expression. ... Let the (*stack*sorting) complexity of π, denoted ssc π, be the smallest k such that π is k-*stack**sortable*. ...##
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Catalan and Schröder permutations sortable by two restricted stacks
[article]

2020
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arXiv
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pre-print

In this work we study pattern avoiding machines where the first

arXiv:2004.01812v2
fatcat:5dphlxwvxvbc7hr7pjbewbxwoa
*stack*avoids a pair of patterns of length 3 and investigate those pairs for which*sortable**permutations*are counted by the (binomial transform ... They consist of two restricted*stacks*in series, ruled by a right-greedy procedure and the*stacks*avoid some specified patterns. ... A*permutation*π is*sortable*using a classical*stack*(that is, a 21-avoiding*stack*) if and only if π avoids the pattern 231. Let T be a set of patterns. ...##
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The generating function of two-stack sortable permutations by descents is real-rooted
[article]

2012
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arXiv
*
pre-print

The paper is withdrawn since the results are included in arXiv:math/0403364.

arXiv:math/0303149v3
fatcat:3ly4mr3ccjgxlc5ozq6ig7hthi
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