关于多集的3-分区的一些注释

Q2 Mathematics
Dorin Andrica, Ovidiu Bagdasar
{"title":"关于多集的3-分区的一些注释","authors":"Dorin Andrica,&nbsp;Ovidiu Bagdasar","doi":"10.1016/j.endm.2018.11.001","DOIUrl":null,"url":null,"abstract":"<div><p>Partitions play an important role in numerous combinatorial optimization problems. Here we introduce the number of ordered 3-partitions of a multiset M having equal sums denoted by S(m<sub>1</sub>,…, m<sub>n</sub>; <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>,…, <span><math><msub><mrow><mi>α</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>), for which we find the generating function and give a useful integral formula. Some recurrence formulae are then established and new integer sequences are added to OEIS, which are related to the number of solutions for the 3-signum equation.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.11.001","citationCount":"6","resultStr":"{\"title\":\"Some remarks on 3-partitions of multisets\",\"authors\":\"Dorin Andrica,&nbsp;Ovidiu Bagdasar\",\"doi\":\"10.1016/j.endm.2018.11.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Partitions play an important role in numerous combinatorial optimization problems. Here we introduce the number of ordered 3-partitions of a multiset M having equal sums denoted by S(m<sub>1</sub>,…, m<sub>n</sub>; <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>,…, <span><math><msub><mrow><mi>α</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>), for which we find the generating function and give a useful integral formula. Some recurrence formulae are then established and new integer sequences are added to OEIS, which are related to the number of solutions for the 3-signum equation.</p></div>\",\"PeriodicalId\":35408,\"journal\":{\"name\":\"Electronic Notes in Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.endm.2018.11.001\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Notes in Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1571065318301963\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Notes in Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1571065318301963","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 6

摘要

分区在许多组合优化问题中起着重要的作用。这里我们引入一个多集M的有序3分区的数目,它们具有相等的和,记为S(m1,…,mn;α1,…,αn),求出了生成函数,并给出了一个有用的积分公式。然后建立了一些递推公式,并在OEIS中加入了新的整数序列,这些序列与3- sgn方程的解的个数有关。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Some remarks on 3-partitions of multisets

Partitions play an important role in numerous combinatorial optimization problems. Here we introduce the number of ordered 3-partitions of a multiset M having equal sums denoted by S(m1,…, mn; α1,…, αn), for which we find the generating function and give a useful integral formula. Some recurrence formulae are then established and new integer sequences are added to OEIS, which are related to the number of solutions for the 3-signum equation.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Electronic Notes in Discrete Mathematics
Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics
CiteScore
1.30
自引率
0.00%
发文量
0
期刊介绍: Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信