Symmetric Difference-Free and Symmetric Difference-Closed Collections of Sets
A collection of sets is symmetric-difference-free, respectively symmetric difference-closed, if the symmetric difference of any two sets in the collection lies outside, respectively inside, the collection. Recently Buck and Godbole (Size-maximal symmetric difference-free families of subsets of [n],...
| Main Authors: | , |
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| Format: | Journal Article |
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Springer Japan KK
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/3743 |
| _version_ | 1848744315723972608 |
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| author | Gamble, Gregory Simpson, Jamie |
| author_facet | Gamble, Gregory Simpson, Jamie |
| author_sort | Gamble, Gregory |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | A collection of sets is symmetric-difference-free, respectively symmetric difference-closed, if the symmetric difference of any two sets in the collection lies outside, respectively inside, the collection. Recently Buck and Godbole (Size-maximal symmetric difference-free families of subsets of [n], Graphs Combin. (to appear), 2013) investigated such collections and showed, in particular, that the largest symmetric difference-free collection of subsets of an n-set has cardinality 2 n-1. We use group theory to obtain shorter proofs of their results. |
| first_indexed | 2025-11-14T05:59:31Z |
| format | Journal Article |
| id | curtin-20.500.11937-3743 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T05:59:31Z |
| publishDate | 2013 |
| publisher | Springer Japan KK |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-37432017-09-13T14:46:24Z Symmetric Difference-Free and Symmetric Difference-Closed Collections of Sets Gamble, Gregory Simpson, Jamie 05A15 Symmetric difference-free 05D05 Sets Symmetric difference-closed A collection of sets is symmetric-difference-free, respectively symmetric difference-closed, if the symmetric difference of any two sets in the collection lies outside, respectively inside, the collection. Recently Buck and Godbole (Size-maximal symmetric difference-free families of subsets of [n], Graphs Combin. (to appear), 2013) investigated such collections and showed, in particular, that the largest symmetric difference-free collection of subsets of an n-set has cardinality 2 n-1. We use group theory to obtain shorter proofs of their results. 2013 Journal Article http://hdl.handle.net/20.500.11937/3743 10.1007/s00373-013-1388-7 Springer Japan KK restricted |
| spellingShingle | 05A15 Symmetric difference-free 05D05 Sets Symmetric difference-closed Gamble, Gregory Simpson, Jamie Symmetric Difference-Free and Symmetric Difference-Closed Collections of Sets |
| title | Symmetric Difference-Free and Symmetric Difference-Closed Collections of Sets |
| title_full | Symmetric Difference-Free and Symmetric Difference-Closed Collections of Sets |
| title_fullStr | Symmetric Difference-Free and Symmetric Difference-Closed Collections of Sets |
| title_full_unstemmed | Symmetric Difference-Free and Symmetric Difference-Closed Collections of Sets |
| title_short | Symmetric Difference-Free and Symmetric Difference-Closed Collections of Sets |
| title_sort | symmetric difference-free and symmetric difference-closed collections of sets |
| topic | 05A15 Symmetric difference-free 05D05 Sets Symmetric difference-closed |
| url | http://hdl.handle.net/20.500.11937/3743 |