Electronic Notes in Discrete Mathematics最新文献_第2页

Polynomial approximation for the number of all possible endpoints of a random walk on a metric graph 度量图上随机游走的所有可能端点数目的多项式近似

Electronic Notes in Discrete Mathematics Pub Date : 2018-12-01 DOI: 10.1016/j.endm.2018.11.005

Vsevolod Chernyshev, Anton Tolchennikov

引用次数: 8

Weighted t-way Sequences 加权t路序列

Electronic Notes in Discrete Mathematics Pub Date : 2018-12-01 DOI: 10.1016/j.endm.2018.11.007

Bernhard Garn, Dimitris E. Simos

引用次数: 3

Hypergraph Modeling and Visualisation of Complex Co-occurence Networks 复杂共现网络的超图建模与可视化

Electronic Notes in Discrete Mathematics Pub Date : 2018-12-01 DOI: 10.1016/j.endm.2018.11.011

X. Ouvrard , J.M. Le Goff , S. Marchand-Maillet

引用次数: 5

On some new arithmetic functions involving prime divisors and perfect powers 关于一些涉及素数因子和完全幂的新的算术函数

Electronic Notes in Discrete Mathematics Pub Date : 2018-12-01 DOI: 10.1016/j.endm.2018.11.002

Ovidiu Bagdasar, Ralph Tatt

{"title":"On some new arithmetic functions involving prime divisors and perfect powers","authors":"Ovidiu Bagdasar, Ralph Tatt","doi":"10.1016/j.endm.2018.11.002","DOIUrl":"10.1016/j.endm.2018.11.002","url":null,"abstract":"<div><p>Integer division and perfect powers play a central role in numerous mathematical results, especially in number theory. Classical examples involve perfect squares like in Pythagora's theorem, or higher perfect powers as the conjectures of Fermat (solved in 1994 by A. Wiles [Wiles, A.J., Modular elliptic curves and Fermat's Last Theorem, Annals of Mathematics, 141 (1995), 443–551.]) or Catalan (solved in 2002 by P. Mihăilescu [Mihăilescu, P., Primary cyclotomic units and a proof of Catalan's conjecture, J. Reine Angew. Math., 572 (2004), 167–195.]). The purpose of this paper is two-fold. First, we present some new integer sequences <span><math><mi>a</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>, counting the positive integers smaller than <em>n</em>, having a maximal prime factor. We introduce an arithmetic function counting the number of perfect powers <span><math><msup><mrow><mi>i</mi></mrow><mrow><mi>j</mi></mrow></msup></math></span> obtained for <span><math><mn>1</mn><mo>≤</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>≤</mo><mi>n</mi></math></span>. Along with some properties of this function, we present the sequence A303748, which was recently added to the Online Encyclopedia of Integer Sequences (OEIS) [The On-Line Encyclopedia of Integer Sequences, <span>http://oeis.org</span><svg><path></path></svg>, OEIS Foundation Inc. 2011.]. Finally, we discuss some other novel integer sequences.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.11.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115376671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

On an arithmetic triangle of numbers arising from inverses of analytic functions 论由解析函数的逆产生的算术三角形

Electronic Notes in Discrete Mathematics Pub Date : 2018-12-01 DOI: 10.1016/j.endm.2018.11.003

Armen G. Bagdasaryan, Ovidiu Bagdasar

引用次数: 0

Some remarks on 3-partitions of multisets 关于多集的3-分区的一些注释

Electronic Notes in Discrete Mathematics Pub Date : 2018-12-01 DOI: 10.1016/j.endm.2018.11.001

Dorin Andrica, Ovidiu Bagdasar

引用次数: 6

Algebraic Techniques for Covering Arrays and related Structures 覆盖数组和相关结构的代数技术

Electronic Notes in Discrete Mathematics Pub Date : 2018-12-01 DOI: 10.1016/j.endm.2018.11.008

Bernhard Garn, Dimitris E. Simos

引用次数: 3

On Bounds for Quantum Error Correcting Codes over EJ-Integers j -整数上量子纠错码的界

Electronic Notes in Discrete Mathematics Pub Date : 2018-12-01 DOI: 10.1016/j.endm.2018.11.015

Eda Yildiz

{"title":"On Bounds for Quantum Error Correcting Codes over EJ-Integers","authors":"Eda Yildiz","doi":"10.1016/j.endm.2018.11.015","DOIUrl":"10.1016/j.endm.2018.11.015","url":null,"abstract":"<div><p>There are some differences between quantum and classical error corrections [Nielsen M.A., and I.L. Chuang, “Quantum Computation and Quantum Information”, Cambridge University Press, Cambridge, 2002.]. Hence, these differences should be considered when a new procedure is performed. In our recent study, we construct new quantum error correcting codes over different mathematical structures. The classical codes over Eisenstein-Jacobi(EJ) integers are mentioned in [Huber, K., “<em>Codes over Eisenstein-Jacobi integers</em>”, Contemporary Mathematics <strong>168</strong> (1994), 165.]. There is an efficient algorithm for the encoding and decoding procedures of these codes [Huber, K., “<em>Codes over Eisenstein-Jacobi integers</em>”, Contemporary Mathematics <strong>168</strong> (1994), 165.]. For coding over two-dimensional signal spaces like QAM signals, block codes over these integers <em>p</em> = 7, 13, 19, 31, 37, 43, 61, … can be useful [Dong, X., C.B. Soh, E. Gunawan and L. Tang, “<em>Groups of Algebraic Integers used for Coding QAM Signals</em>”, Information Theory, IEEE <strong>44</strong> (1998), 1848–1860.]. Thus, in this study, we introduce quantum error correcting codes over EJ-integers. This type of quantum codes may lead to codes with some new and good parameters.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.11.015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125641415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A hybrid heuristic for the multi-activity tour scheduling problem 多活动旅行调度问题的混合启发式算法

Electronic Notes in Discrete Mathematics Pub Date : 2018-08-01 DOI: 10.1016/j.endm.2018.07.043

Stefania Pan , Mahuna Akplogan, Nora Touati, Lucas Létocart, Roberto Wolfler Calvo, Louis-Martin Rousseau

引用次数: 3

An integer linear programming model for the constrained shortest path tour problem 约束最短路径漫游问题的整数线性规划模型

Electronic Notes in Discrete Mathematics Pub Date : 2018-08-01 DOI: 10.1016/j.endm.2018.07.019

Rafael Castro de Andrade, Rommel Dias Saraiva

引用次数: 17