scholarly journals Flip-sort and combinatorial aspects of pop-stack sorting

2021 ◽  
Vol vol. 22 no. 2, Permutation... (Special issues) ◽  
Author(s):  
Andrei Asinowski ◽  
Cyril Banderier ◽  
Benjamin Hackl
Keyword(s):  
Lattice Paths ◽  
Permutation Patterns ◽  
Seminal Work ◽  
Sorting Algorithms ◽  
Stack Sorting

Flip-sort is a natural sorting procedure which raises fascinating combinatorial questions. It finds its roots in the seminal work of Knuth on stack-based sorting algorithms and leads to many links with permutation patterns. We present several structural, enumerative, and algorithmic results on permutations that need few (resp. many) iterations of this procedure to be sorted. In particular, we give the shape of the permutations after one iteration, and characterize several families of permutations related to the best and worst cases of flip-sort. En passant, we also give some links between pop-stack sorting, automata, and lattice paths, and introduce several tactics of bijective proofs which have their own interest. Comment: This v3 just updates the journal reference, according to the publisher wish

scholarly journals Finding and Counting Permutations via CSPs

Algorithmica ◽  
2021 ◽  
Author(s):  
Benjamin Aram Berendsohn ◽  
László Kozma ◽  
Dániel Marx
Keyword(s):  
Constraint Satisfaction ◽  
Polynomial Space ◽  
Permutation Patterns ◽  
Counting Problem ◽  
Exponential Time ◽  
Running Time ◽  
Algorithmic Question ◽  
Stack Sorting ◽  
Exponential Time Algorithms ◽  
New Algorithms

AbstractPermutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this area is deciding whether a given permutation of length n contains a given pattern of length k. In this work we give two new algorithms for this well-studied problem, one whose running time is $$n^{k/4 + o(k)}$$ n k / 4 + o ( k ) , and a polynomial-space algorithm whose running time is the better of $$O(1.6181^n)$$ O ( 1 . 6181 n ) and $$O(n^{k/2 + 1})$$ O ( n k / 2 + 1 ) . These results improve the earlier best bounds of $$n^{0.47k + o(k)}$$ n 0.47 k + o ( k ) and $$O(1.79^n)$$ O ( 1 . 79 n ) due to Ahal and Rabinovich (2000) resp. Bruner and Lackner (2012) and are the fastest algorithms for the problem when $$k \in \varOmega (\log {n})$$ k ∈ Ω ( log n ) . We show that both our new algorithms and the previous exponential-time algorithms in the literature can be viewed through the unifying lens of constraint-satisfaction. Our algorithms can also count, within the same running time, the number of occurrences of a pattern. We show that this result is close to optimal: solving the counting problem in time $$f(k) \cdot n^{o(k/\log {k})}$$ f ( k ) · n o ( k / log k ) would contradict the exponential-time hypothesis (ETH). For some special classes of patterns we obtain improved running times. We further prove that 3-increasing (4321-avoiding) and 3-decreasing (1234-avoiding) permutations can, in some sense, embed arbitrary permutations of almost linear length, which indicates that a sub-exponential running time is unlikely with the current techniques, even for patterns from these restricted classes.

scholarly journals A Survey of Stack-Sorting Disciplines

10.37236/1693 ◽  
2003 ◽  
Vol 9 (2) ◽  
Author(s):  
Miklós Bóna
Keyword(s):  
Graph Theory ◽  
Planar Graph ◽  
Young Tableau ◽  
Simplicial Complexes ◽  
Permutation Patterns ◽  
Stack Sorting

We review the various ways that stacks, their variations and their combinations, have been used as sorting devices. In particular, we show that they have been a key motivator for the study of permutation patterns. We also show that they have connections to other areas in combinatorics such as Young tableau, planar graph theory, and simplicial complexes.

A Court in Decline? Examining the Regality Court Records of Melrose, Roxburghshire, 1657–84

2020 ◽  
Vol 40 (1) ◽  
pp. 1-16
Author(s):  
Vivienne Dunstan
Keyword(s):  
Seventeenth Century ◽  
Local Community ◽  
Local Population ◽  
Local Area ◽  
Vital Role ◽  
Local Communities ◽  
Court Records ◽  
Seminal Work

McIntyre, in his seminal work on Scottish franchise courts, argues that these courts were in decline in this period, and of little relevance to their local population. 1 But was that really the case? This paper explores that question, using a particularly rich set of local court records. By analysing the functions and significance of one particular court it assesses the role of this one court within its local area, and considers whether it really was in decline at this time, or if it continued to perform a vital role in its local community. The period studied is the mid to late seventeenth century, a period of considerable upheaval in Scottish life, that has attracted considerable attention from scholars, though often less on the experiences of local communities and people.

John Henry Newman

2018 ◽  
Author(s):  
Michael D. Hurley
Keyword(s):  
John Henry Newman ◽  
Seminal Work ◽  
Non Fiction ◽  
Prose Style ◽  
Definition Of

Newman has been much vaunted as a ‘master’ of non-fiction prose style, and justly so. His felicity of phrasing is astonishing: so precise, so elegant, so vivid. This chapter admires Newman’s stylistic achievements too, but with a view to explaining why Newman himself baulked at such praise, by insisting instead on the importance of veracity over verbalism. While a number of different writings by Newman are surveyed in the course of the chapter, the argument comes to focus in particular on his seminal work of faith, Grammar of Assent, a book that took him some twenty years to write, which almost killed him, and which best exemplifies his suggestive but enigmatic definition of ‘style’ as ‘a thinking out into language’.

Ecofeminist Biblical Hermeneutics for Cyborgs and the Story of Jezebel

2020 ◽  
pp. 295-311
Author(s):  
Arthur W. Walker-Jones
Keyword(s):  
Digital Media ◽  
Hebrew Bible ◽  
Digital Humanities ◽  
Environmental Crisis ◽  
Biblical Hermeneutics ◽  
Biblical Story ◽  
Seminal Work ◽  
Feminist Interpretation ◽  
Digital Cultures

This chapter examines the Jezebel.com website as a feminist interpretation of the biblical story of Jezebel, in order to discuss the ways digital media make reading more transparent, intertextual, and holistic. Donna Haraway’s article “A Manifesto for Cyborgs” is a seminal work for both ecofeminism and the digital humanities. This articles uses her understanding of the cyborg and naturecultures to argue that Jezebel has become a cyborg online. Cyborgs and digital media could be used to reinforce the nature–culture dualism that is related to male–female dualism and has legitimated patriarchy and the environmental crisis. This chapter, therefore, argues that the identification of cyborg naturecultures in reading both the biblical stories and digital cultures is particularly important for ecofeminist approaches to the Hebrew Bible.

scholarly journals Combinatorics on lattice paths in strips

2021 ◽  
Vol 94 ◽  
pp. 103310
Author(s):  
Nancy S.S. Gu ◽  
Helmut Prodinger
Keyword(s):  
Lattice Paths

Rhetoric beyond Arguments: Thinking about the Role of Fictional Audiences in Plato’s Gorgias

Elenchos ◽  
2020 ◽  
Vol 41 (2) ◽  
pp. 217-243
Author(s):  
Dora Suarez
Keyword(s):  
Crucial Step ◽  
Universal Audience ◽  
Seminal Work ◽  
New Rhetoric ◽  
Chaim Perelman ◽  
The Way

AbstractIn this piece, I propose a reading of Plato’s Gorgias that pays special attention to the role that the fictional audience plays in the unfolding of the dialogue. To this end, I use some of the insights that Chaïm Perelman and Lucie Olbrechts–Tyteca conveyed in their seminal work, The New Rhetoric: A Treatise on Argumentation in order to argue that thinking about the way in which Socrates’ arguments are shaped by the different audiences that Gorgias, Polus, and Callicles aim to address and represent provides us with a new hermeneutical understanding of what is at stake in each of the different interactions Socrates engages in throughout the dialogue. In unpacking the way in which Socrates appropriates Gorgias’ particular audience, transforms Polus’ universal audience, and challenges Callicles’ elite audience, I provide an outline of the difficulties that Plato’s Socrates has to overcome in order to achieve the ‘community of minds’ that Perelman and Olbrechts–Tyteca identify as the bedrock of fruitful argumentation. Having done this, in the last section I turn to Plato’s Phaedrus, for the purpose of making evident that thinking about Plato’s deployment of rhetorical audiences is a crucial step in the effort to expose the implicit continuity that links the discussion of rhetoric delivered by the Gorgias to that of the Phaedrus.

Performance evaluation of LAN sorting algorithms

1987 ◽  
Vol 15 (1) ◽  
pp. 226-233
Author(s):  
Mohamed Salehmohamed ◽  
W. S. Luk ◽  
Joseph G. Peters
Keyword(s):  
Performance Evaluation ◽  
Sorting Algorithms

Average time behavior of distributive sorting algorithms

Computing ◽  
1981 ◽  
Vol 26 (1) ◽  
pp. 1-7 ◽  
Author(s):  
L. Devroye ◽  
T. Klincsek
Keyword(s):  
Time Behavior ◽  
Sorting Algorithms

Boundaries in the Making: Transformations in Erving Goffman’s Total Institution through the Case of a Female Benedictine Monastery

Sociology ◽  
2021 ◽  
pp. 003803852110115
Author(s):  
Anna Clot-Garrell
Keyword(s):  
Empirical Research ◽  
Total Institution ◽  
Erving Goffman ◽  
Seminal Work ◽  
Total Institutions ◽  
Late Modern

Total institutions have undergone profound changes since Erving Goffman published his seminal work Asylums in 1961. This article explores the persistence and transformation of total institutions under late-modern conditions. Based upon empirical research conducted in a female Benedictine monastery, I analyse changes in the physically bounded structure of a total institution. Specifically, I address the trend towards greater permeability and flexibility of enclosed total spaces. Inspired by Georg Simmel’s spatial insights, I examine how boundaries are historically reshaped through changing relations of distance and proximity to wider society, and how these shifts alter the material expression and configuration of power that originally characterised the monastery’s totality. This article claims the ongoing relevance of Goffman’s conceptualisation to accommodate such modifications and illustrates how, in certain cases, adaptations of total institutions to contemporary conditions can be understood as involving the reconfiguration, rather than the dismantling, of totality.

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