Selfishness of convex bodies and discrete point sets
Let F be a family of sets in Rd. A set M⊂Rd is called F-convex if for any pair of distinct points x,y∈M, there is a set F∈F such that x,y∈F and F⊂M. A family F of compact sets is called complete if F contains all compact F-convex sets. Generalizing the definition in Yuan and Zamfirescu (2016), a com...
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| Published in | European journal of combinatorics Vol. 80; pp. 416 - 431 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.08.2019
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| Online Access | Get full text |
| ISSN | 0195-6698 1095-9971 |
| DOI | 10.1016/j.ejc.2018.02.012 |
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| Abstract | Let F be a family of sets in Rd. A set M⊂Rd is called F-convex if for any pair of distinct points x,y∈M, there is a set F∈F such that x,y∈F and F⊂M.
A family F of compact sets is called complete if F contains all compact F-convex sets. Generalizing the definition in Yuan and Zamfirescu (2016), a compact set K will be called selfish, if the family FK of all sets similar to K contains all compact FK-convex sets.
In this paper, we investigate the selfishness of rectangles, isosceles triangles, regular n-gons, and some finite sets. |
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| AbstractList | Let F be a family of sets in Rd. A set M⊂Rd is called F-convex if for any pair of distinct points x,y∈M, there is a set F∈F such that x,y∈F and F⊂M.
A family F of compact sets is called complete if F contains all compact F-convex sets. Generalizing the definition in Yuan and Zamfirescu (2016), a compact set K will be called selfish, if the family FK of all sets similar to K contains all compact FK-convex sets.
In this paper, we investigate the selfishness of rectangles, isosceles triangles, regular n-gons, and some finite sets. |
| Author | Zamfirescu, Tudor Zhang, Yue Yuan, Liping |
| Author_xml | – sequence: 1 givenname: Liping surname: Yuan fullname: Yuan, Liping email: lpyuan@hebtu.edu.cn organization: College of Mathematics and Information Science, Hebei Normal University, 050024 Shijiazhuang, PR China – sequence: 2 givenname: Tudor surname: Zamfirescu fullname: Zamfirescu, Tudor email: tudor.zamfirescu@mathematik.uni-dortmund.de organization: College of Mathematics and Information Science, Hebei Normal University, 050024 Shijiazhuang, PR China – sequence: 3 givenname: Yue surname: Zhang fullname: Zhang, Yue email: zhangyue0309@126.com organization: College of Mathematics and Information Science, Hebei Normal University, 050024 Shijiazhuang, PR China |
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| References | Mayer (b15) 1935; 39 Yuan, Zamfirescu (b18) 2017; 18 Magazanik, Perles (b14) 2007; 37 Böröczky Jr. (b3) 1990; 34 Breen (b5) 2012; 53 Zamfirescu (b20) 2014; 21 Breen (b6) 2014; 87 Magazanik, Perles (b13) 2007; 160 Yuan, Zamfirescu (b17) 2016; 23 Blind, Valette, Zamfirescu (b2) 1980; 9 Farber, Jamison (b11) 1987; 66 Bezdek, Lángi, Naszódi, Papez (b1) 2007; 38 Bruckner, Bruckner (b8) 1964; 2 Duchet (b10) 1988; 44 Lángi, Naszódi, Talata (b12) 2013; 85 Breen (b4) 2010; 51 Changat, Mathew (b9) 1999; 206 Yuan, Zamfirescu (b16) 2015; 22 Breen (b7) 2015; 89 Yuan, Zamfirescu, Zhang (b19) 2017; 33 Lángi (10.1016/j.ejc.2018.02.012_b12) 2013; 85 Magazanik (10.1016/j.ejc.2018.02.012_b14) 2007; 37 Yuan (10.1016/j.ejc.2018.02.012_b17) 2016; 23 Breen (10.1016/j.ejc.2018.02.012_b6) 2014; 87 Farber (10.1016/j.ejc.2018.02.012_b11) 1987; 66 Breen (10.1016/j.ejc.2018.02.012_b7) 2015; 89 Yuan (10.1016/j.ejc.2018.02.012_b19) 2017; 33 Breen (10.1016/j.ejc.2018.02.012_b5) 2012; 53 Yuan (10.1016/j.ejc.2018.02.012_b18) 2017; 18 Zamfirescu (10.1016/j.ejc.2018.02.012_b20) 2014; 21 Breen (10.1016/j.ejc.2018.02.012_b4) 2010; 51 Duchet (10.1016/j.ejc.2018.02.012_b10) 1988; 44 Magazanik (10.1016/j.ejc.2018.02.012_b13) 2007; 160 Mayer (10.1016/j.ejc.2018.02.012_b15) 1935; 39 Yuan (10.1016/j.ejc.2018.02.012_b16) 2015; 22 Bruckner (10.1016/j.ejc.2018.02.012_b8) 1964; 2 Bezdek (10.1016/j.ejc.2018.02.012_b1) 2007; 38 Blind (10.1016/j.ejc.2018.02.012_b2) 1980; 9 Changat (10.1016/j.ejc.2018.02.012_b9) 1999; 206 Böröczky Jr. (10.1016/j.ejc.2018.02.012_b3) 1990; 34 |
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| Snippet | Let F be a family of sets in Rd. A set M⊂Rd is called F-convex if for any pair of distinct points x,y∈M, there is a set F∈F such that x,y∈F and F⊂M.
A family F... |
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| Title | Selfishness of convex bodies and discrete point sets |
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