{"title":"积分凸集的 Shapley-Folkman 型定理","authors":"Kazuo Murota , Akihisa Tamura","doi":"10.1016/j.dam.2024.08.015","DOIUrl":null,"url":null,"abstract":"<div><p>The Shapley–Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex sets, M<span><math><msup><mrow></mrow><mrow><mi>♮</mi></mrow></msup></math></span>-convex sets, and L<span><math><msup><mrow></mrow><mrow><mi>♮</mi></mrow></msup></math></span>-convex sets, which are major classes of discrete convex sets in discrete convex analysis.</p></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"360 ","pages":"Pages 42-50"},"PeriodicalIF":1.0000,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0166218X24003731/pdfft?md5=d073edec49748d4427d0a7829a4d4a66&pid=1-s2.0-S0166218X24003731-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Shapley–Folkman-type theorem for integrally convex sets\",\"authors\":\"Kazuo Murota , Akihisa Tamura\",\"doi\":\"10.1016/j.dam.2024.08.015\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The Shapley–Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex sets, M<span><math><msup><mrow></mrow><mrow><mi>♮</mi></mrow></msup></math></span>-convex sets, and L<span><math><msup><mrow></mrow><mrow><mi>♮</mi></mrow></msup></math></span>-convex sets, which are major classes of discrete convex sets in discrete convex analysis.</p></div>\",\"PeriodicalId\":50573,\"journal\":{\"name\":\"Discrete Applied Mathematics\",\"volume\":\"360 \",\"pages\":\"Pages 42-50\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-08-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0166218X24003731/pdfft?md5=d073edec49748d4427d0a7829a4d4a66&pid=1-s2.0-S0166218X24003731-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0166218X24003731\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X24003731","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Shapley–Folkman-type theorem for integrally convex sets
The Shapley–Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex sets, M-convex sets, and L-convex sets, which are major classes of discrete convex sets in discrete convex analysis.
期刊介绍：
The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal.
Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.
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