scholarly journals On additive combinatorics of permutations of ℤn

2014 ◽  
Vol Vol. 16 no. 2 (PRIMA 2013) ◽  
Author(s):  
L. Sunil Chandran ◽  
Deepak Rajendraprasad ◽  
Nitin Singh
Keyword(s):  
Maximum Size ◽  
Extremal Problems ◽  
Additive Combinatorics ◽  
Special Issue ◽  
Prime Divisors ◽  
Ring Of Integers ◽  
Euler’S Totient Function ◽  
International Audience ◽  
Addition And Subtraction

Special issue PRIMA 2013 International audience Let ℤ<sub>n</sub> denote the ring of integers modulo n. A permutation of ℤ<sub>n</sub> is a sequence of n distinct elements of ℤ<sub>n</sub>. Addition and subtraction of two permutations is defined element-wise. In this paper we consider two extremal problems on permutations of ℤ<sub>n</sub>, namely, the maximum size of a collection of permutations such that the sum of any two distinct permutations in the collection is again a permutation, and the maximum size of a collection of permutations such that no sum of two distinct permutations in the collection is a permutation. Let the sizes be denoted by s(n) and t(n) respectively. The case when n is even is trivial in both the cases, with s(n)=1 and t(n)=n!. For n odd, we prove (nφ(n))/2<sup>k</sup>≤s(n)≤n!· 2<sup>-(n-1)/2</sup>((n-1)/2)! and 2<sup>(n-1)/2</sup>·(n-1 / 2)!≤t(n)≤ 2<sup>k</sup>·(n-1)!/φ(n), where k is the number of distinct prime divisors of n and φ is the Euler's totient function.

scholarly journals Special Issue on Visualisations in Historical Linguistics: Introduction

2020 ◽  
Vol Special issue on... ◽  
Author(s):  
Benjamin Molineaux ◽  
Bettelou Los ◽  
Martti Mäkinen
Keyword(s):  
Historical Linguistics ◽  
Data Visualisation ◽  
Complex Materials ◽  
Special Issue ◽  
The Core ◽  
Methodological Research ◽  
International Audience ◽  
Introductory Paper ◽  
The Individual ◽  
Historical Periods

International audience The advent of ever-larger and more diverse historical corpora for different historical periods and linguistic varieties has led to the impossibility of obtaining simple, direct-and yet balancedrepresentations of the core patterns in the data. In order to draw insights from heterogeneous and complex materials of this type, historical linguists have begun to reach for a growing number of data visualisation techniques, from the statistical, to the cartographical, the network-based and beyond. An exploration of the state of this art was the objective of a workshop at the 2018 International Conference on English Historical Linguistics, from whence most of the materials of this Special Issue are drawn. This brief introductory paper outlines the background and relevance of this line of methodological research and presents a summary of the individual papers that make up the collection.

scholarly journals On some over primes

1994 ◽  
Vol Volume 17 ◽  
Author(s):  
J W Sander
Keyword(s):  
Binomial Coefficients ◽  
Log P ◽  
Prime Divisors ◽  
International Audience

International audience It will be shown that, for any $\delta > 0$, \[ {\sum_{p\leq n}}^* \; \frac{\log p}{p} = \frac{1}{2} \log n + O\Big((\log n)^{\frac{5}{6}+\delta}\Big), \] where (*) restricts the summation to those primes $p$, which satisfy $n = kp+r$ for some integers $k$ and $r$, $p/2 < r < p$. This result is connected with questions concerning prime divisors of binomial coefficients.

scholarly journals On the minimal distance of a polynomial code

2011 ◽  
Vol Vol. 13 no. 4 ◽  
Author(s):  
Peter Pal Pach ◽  
Csaba Szabo
Keyword(s):  
Finite Subset ◽  
60Th Birthday ◽  
Theoretical Problem ◽  
Minimal Distance ◽  
Distribution Of Primes ◽  
Special Issue ◽  
Theoretical Methods ◽  
Algorithms And Complexity ◽  
International Audience ◽  
Special Case

special issue in honor of Laci Babai's 60th birthday: Combinatorics, Groups, Algorithms, and Complexity International audience For a polynomial f(x) is an element of Z(2)[x] it is natural to consider the near-ring code generated by the polynomials f circle x, f circle x(2) ,..., f circle x(k) as a vectorspace. It is a 19 year old conjecture of Gunter Pilz that for the polynomial f (x) - x(n) broken vertical bar x(n-1) broken vertical bar ... broken vertical bar x the minimal distance of this code is n. The conjecture is equivalent to the following purely number theoretical problem. Let (m) under bar = \1, 2 ,..., m\ and A subset of N be an arbitrary finite subset of N. Show that the number of products that occur odd many times in (n) under bar. A is at least n. Pilz also formulated the conjecture for the special case when A = (k) under bar. We show that for A = (k) under bar the conjecture holds and that the minimal distance of the code is at least n/(log n)(0.223). While proving the case A = (k) under bar we use different number theoretical methods depending on the size of k (respect to n). Furthermore, we apply several estimates on the distribution of primes.

scholarly journals The extended equivalence and equation solvability problems for groups

2011 ◽  
Vol Vol. 13 no. 4 ◽  
Author(s):  
Gabor Horvath ◽  
Csaba Szabo
Keyword(s):  
Polynomial Time ◽  
Equivalence Problem ◽  
Nilpotent Groups ◽  
60Th Birthday ◽  
Special Issue ◽  
Algorithms And Complexity ◽  
International Audience ◽  
Solvability Problem ◽  
Np Complete ◽  
Equation Solvability

special issue in honor of Laci Babai's 60th birthday: Combinatorics, Groups, Algorithms, and Complexity International audience We prove that the extended equivalence problem is solvable in polynomial time for finite nilpotent groups, and coNP-complete, otherwise. We prove that the extended equation solvability problem is solvable in polynomial time for finite nilpotent groups, and NP-complete, otherwise.

scholarly journals Separating the k-party communication complexity hierarchy: an application of the Zarankiewicz problem

2011 ◽  
Vol Vol. 13 no. 4 ◽  
Author(s):  
Thomas P. Hayes
Keyword(s):  
Positive Integer ◽  
Open Problem ◽  
Communication Complexity ◽  
60Th Birthday ◽  
Equal Size ◽  
Special Issue ◽  
Algorithms And Complexity ◽  
International Audience ◽  
Zarankiewicz Problem ◽  
Complexity Hierarchy

special issue in honor of Laci Babai's 60th birthday: Combinatorics, Groups, Algorithms, and Complexity International audience For every positive integer k, we construct an explicit family of functions f : \0, 1\(n) -\textgreater \0, 1\ which has (k + 1) - party communication complexity O(k) under every partition of the input bits into k + 1 parts of equal size, and k-party communication complexity Omega (n/k(4)2(k)) under every partition of the input bits into k parts. This improves an earlier hierarchy theorem due to V. Grolmusz. Our construction relies on known explicit constructions for a famous open problem of K. Zarankiewicz, namely, to find the maximum number of edges in a graph on n vertices that does not contain K-s,K-t as a subgraph.

scholarly journals Some results on counting roots of polynomials and the Sylvester resultant.

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Michael Monagan ◽  
Baris Tuncer
Keyword(s):  
Diophantine Equations ◽  
Multivariate Polynomials ◽  
Ring Of Integers ◽  
Sylvester Resultant ◽  
International Audience ◽  
Roots Of Polynomials ◽  
Polynomial Gcd ◽  
Roots Of A Polynomial

International audience We present two results, the first on the distribution of the roots of a polynomial over the ring of integers modulo n and the second on the distribution of the roots of the Sylvester resultant of two multivariate polynomials. The second result has application to polynomial GCD computation and solving polynomial diophantine equations.

scholarly journals Grammatical compression: compressed equivalence and other problems

2010 ◽  
Vol Vol. 12 no. 4 ◽  
Author(s):  
Alberto Bertoni ◽  
Roberto Radicioni
Keyword(s):  
Strategic Games ◽  
Special Issue ◽  
Ability To Work ◽  
Inclusion Problems ◽  
Polynomial Time Algorithms ◽  
Straight Line ◽  
International Audience ◽  
Context Free ◽  
Compressed Data ◽  
Straight Line Programs

special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications International audience In this work, we focus our attention to algorithmic solutions for problems where the instances are presented as straight-line programs on a given algebra. In our exposition, we try to survey general results by presenting some meaningful examples; moreover, where possible, we outline the proofs in order to give an insight of the methods and the techniques. We recall some recent results for the problem PosSLP, consisting of deciding if the integer defined by a straight-line program on the ring Z is greater than zero; we discuss some implications in the areas of numerical analysis and strategic games. Furthermore, we propose some methods for reducing Compressed Word Problem from an algebra to another; reductions from trace monoids to the semiring of nonnegative integers are exhibited and polynomial time algorithms for compressed equivalence in monoids related to Dyck reductions are shown. Finally, we consider inclusion problems for context-free languages, proving how in some cases efficient algorithms for these problems benefit from the ability to work with compressed data.

scholarly journals Noneffective Regularity of Equality Languages and Bounded Delay Morphisms

2010 ◽  
Vol Vol. 12 no. 4 ◽  
Author(s):  
Juhani Karhumaki ◽  
Aleksi Saarela
Keyword(s):  
Special Issue ◽  
Bounded Delay ◽  
International Audience

special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications International audience We give an instance of a class of morphisms for which it is easy to prove that their equality set is regular, but its emptiness is still undecidable. The class is that of bounded delay 2 morphisms.

scholarly journals A randomized algorithm for finding a maximum clique in the visibility graph of a simple polygon

2015 ◽  
Vol Vol. 17 no. 1 (Discrete Algorithms) ◽  
Author(s):  
Sergio Cabello ◽  
Maria Saumell
Keyword(s):  
Hamiltonian Cycle ◽  
Randomized Algorithm ◽  
Maximum Clique ◽  
Simple Polygon ◽  
Maximum Size ◽  
Visibility Graph ◽  
Probability Of Error ◽  
Discrete Algorithms ◽  
International Audience ◽  
Previous Algorithm

Discrete Algorithms International audience We present a randomized algorithm to compute a clique of maximum size in the visibility graph G of the vertices of a simple polygon P. The input of the problem consists of the visibility graph G, a Hamiltonian cycle describing the boundary of P, and a parameter δ∈(0,1) controlling the probability of error of the algorithm. The algorithm does not require the coordinates of the vertices of P. With probability at least 1-δ the algorithm runs in O( |E(G)|2 / ω(G) log(1/δ)) time and returns a maximum clique, where ω(G) is the number of vertices in a maximum clique in G. A deterministic variant of the algorithm takes O(|E(G)|2) time and always outputs a maximum size clique. This compares well to the best previous algorithm by Ghosh et al. (2007) for the problem, which is deterministic and runs in O(|V(G)|2 |E(G)|) time.

scholarly journals INTRODUCTION TO SPECIAL ISSUE 3 : 2017

2017 ◽  
Vol 15 (3) ◽  
Author(s):  
Ihsan Zainal Mokthar
Keyword(s):  
Urban Planning ◽  
Online Version ◽  
Special Issue ◽  
Journal Editorial ◽  
International Audience

I am pleased to present to you this Planning Malaysia Journal Volume 15 Issue 3 for your reading pleasure. Since our migration to online version of the Journal, we have successfullyelevated the Journal to higher level. The Journal readership has increased, reaching wider and international audience. The Journal is also gaining recognition from local and foreign scholars. Article submissions have increased three-fold and this year alone we are publishing 5 issues of the Journal, which is unprecedented. This issue also reflects the wider acceptance of the Journal. It includes articles not only from local scholars, but also from foreign scholars. We hoped that the inclusion of articles from foreign scholars would benefits local readers with knowledge of cases and experiences related to urban planning from other countries as well.I would like to thank the Journal Editorial Board and Secretariat for their untiring efforts in the publication of the Journal and also in successfully uplifting the Journal to higher level.Thank you.

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