Topic
Permutation graph
About: Permutation graph is a research topic. Over the lifetime, 1486 publications have been published within this topic receiving 31654 citations.
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Papers
Book•
1 Jan 1980
TL;DR: This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems and remains a stepping stone from which the reader may embark on one of many fascinating research trails.
Abstract: Algorithmic Graph Theory and Perfect Graphs, first published in 1980, has become the classic introduction to the field. This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems. It remains a stepping stone from which the reader may embark on one of many fascinating research trails. The past twenty years have been an amazingly fruitful period of research in algorithmic graph theory and structured families of graphs. Especially important have been the theory and applications of new intersection graph models such as generalizations of permutation graphs and interval graphs. These have lead to new families of perfect graphs and many algorithmic results. These are surveyed in the new Epilogue chapter in this second edition. New edition of the "Classic" book on the topic Wonderful introduction to a rich research area Leading author in the field of algorithmic graph theory Beautifully written for the new mathematician or computer scientist Comprehensive treatment
4,370 citations
TL;DR: In a beautiful but unpublished thesis written in 1972, Patton as discussed by the authors proved the corresponding results for all the groups SL(n, q), as well as for Sp(2m, q) with 2 odd.
1,609 citations
TL;DR: The Romberg integration algorithm has been used with great success by many groups [1, 2], and appears to be among the most generally reliable quadrature methods available.
Abstract: real procedure PCpolynomial (x, n, a); integer n; real x, a; comment PCpolynomial computes values of the Poisson-Charlier polynomial p~(x) defined by L. Carlitz, Characterization of certain sequences of orthogonal polynomials, Portugaliae Mathematica 20 (1961), 43-46: () (:) p~(x) a~12(n~)_ll~ ~ (_1).~ n =. r! a ~ r=0 r • In this algorithm u stands for the successive terms of the summa-tion, s stands for the sum of these terms and all other symbols possess evident meanings. Clearly each term of the summation is obtained from the preceding one by the indicated multiplication ; c:=l; for] := 1 step 1 untilndoc := c X j; for j := 0 step 1 until n-1 do begin u :=-u X (n-j) X (x-j)/(a X (]-~-1)); s := s + u end; PCpolynomial := sqrt(a Tn/c) X s end PCpolynomial integer array a; begin comment SHUFFLE applies a random permutation to the sequence a[i] where i = 1, 2, ... , n. The procedure random is supposed to supply a random element from a large population of real numbers uniformly distributed over the open unit interval 0 < r < 1. The array a is declared to be integer but actually it suffices for its type to agree with that of the variable b (in the procedure body); integer i, j; real b; for i := n step-1 until 2 do begin 3" := entier (i X random-~ 1); b := a[i]; a[i] := a~']; a[]] := b end loop i end SHUFFLE Note. Numbers in brackets following Algorithm titles indicate the subject category for the algorithm, based on the Modified SHARE Classification listing given in the 1Viarch, 1964 issue of the Communications of the ACM. The Romberg integration algorithm has been used with great success by many groups [1, 2], and appears to be among the most generally reliable quadrature methods available. It is, therefore, worth pointing out that it is not entirely foolproof, and that a significant class of integrands exists for which the extrapolated values are poorer estimates of the integral than the corresponding trapezoidal sums. The validity of the Romberg procedure depends upon the possibility of expanding the error of the trapezoidal rule in powers of h 2, where h is the stepsize. One expansion of this type is the Euler-Maclaurin sum formula. An alternative expression may be obtained from the Fourier series expansion. The coefficients of h 2" …
466 citations
Book•
17 Mar 2003TL;DR: This paper presents an overview of black-box groups, a library of nearly linear time algorithms, and large-base groups, which are examples of permutation groups used for generating strong generating sets.
Abstract: 1. Introduction 2. Black-box groups 3. Permutation groups: a complexity overview 4. Bases and strong generating sets 5. Further low-level algorithms 6. A library of nearly linear time algorithms 7. Solvable permutation groups 8. Strong generating tests 9. Backtrack methods 10. Large-base groups.
430 citations
TL;DR: In this paper, a self-contained proof of O'Nan-Scott Theorem for finite primitive permutation groups is given, and the proof is shown to be self-sufficient.
Abstract: We give a self-contained proof of the O'Nan-Scott Theorem for finite primitive permutation groups.
382 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2024 | 4 |
| 2023 | 14 |
| 2022 | 30 |
| 2021 | 11 |
| 2020 | 7 |
| 2019 | 4 |