On Optimal M-Sets Related to Motzkin’s Problem
Let M be a set of positive integers. A set S of nonnegative integers is called an M‐set if a and b∈S, then a−b∉M. If S⊆0,1,…,n is an M−set with the maximal cardinality, then S is called a maximal M−set of 0,1,…,n. If S∩0,1,…,n is a maximal M−set of 0,1,…,n for all integers n≥0, then we call S an opt...
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| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/7457625 |
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| author | Quan-Hui Yang Ting Pan Jian-Dong Wu |
| author_facet | Quan-Hui Yang Ting Pan Jian-Dong Wu |
| author_sort | Quan-Hui Yang |
| collection | DOAJ |
| description | Let M be a set of positive integers. A set S of nonnegative integers is called an M‐set if a and b∈S, then a−b∉M. If S⊆0,1,…,n is an M−set with the maximal cardinality, then S is called a maximal M−set of 0,1,…,n. If S∩0,1,…,n is a maximal M−set of 0,1,…,n for all integers n≥0, then we call S an optimal M−set. In this paper, we study the existence of an optimal M−set. |
| format | Article |
| id | doaj-art-ebff936596f14002b4b6a914fe7b0d61 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ebff936596f14002b4b6a914fe7b0d612025-02-03T01:25:46ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/74576257457625On Optimal M-Sets Related to Motzkin’s ProblemQuan-Hui Yang0Ting Pan1Jian-Dong Wu2School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, ChinaSchool of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, ChinaSchool of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210023, ChinaLet M be a set of positive integers. A set S of nonnegative integers is called an M‐set if a and b∈S, then a−b∉M. If S⊆0,1,…,n is an M−set with the maximal cardinality, then S is called a maximal M−set of 0,1,…,n. If S∩0,1,…,n is a maximal M−set of 0,1,…,n for all integers n≥0, then we call S an optimal M−set. In this paper, we study the existence of an optimal M−set.http://dx.doi.org/10.1155/2020/7457625 |
| spellingShingle | Quan-Hui Yang Ting Pan Jian-Dong Wu On Optimal M-Sets Related to Motzkin’s Problem Journal of Mathematics |
| title | On Optimal M-Sets Related to Motzkin’s Problem |
| title_full | On Optimal M-Sets Related to Motzkin’s Problem |
| title_fullStr | On Optimal M-Sets Related to Motzkin’s Problem |
| title_full_unstemmed | On Optimal M-Sets Related to Motzkin’s Problem |
| title_short | On Optimal M-Sets Related to Motzkin’s Problem |
| title_sort | on optimal m sets related to motzkin s problem |
| url | http://dx.doi.org/10.1155/2020/7457625 |
| work_keys_str_mv | AT quanhuiyang onoptimalmsetsrelatedtomotzkinsproblem AT tingpan onoptimalmsetsrelatedtomotzkinsproblem AT jiandongwu onoptimalmsetsrelatedtomotzkinsproblem |