Symmetric complete sum-free sets in cyclic groups
We present constructions of symmetric complete sum-free sets in general finite cyclic groups. It is shown that the relative sizes of the sets are dense in [0, 1/3], answering a question of Cameron, and that the number of those contained in the cyclic group of order n is exponential in n . For primes...
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| Veröffentlicht in: | Israel journal of mathematics 2018-08, Vol.227 (2), p.931-956 |
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| container_title | Israel journal of mathematics |
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| creator | Haviv, Ishay Levy, Dan |
| description | We present constructions of symmetric complete sum-free sets in general finite cyclic groups. It is shown that the relative sizes of the sets are dense in [0, 1/3], answering a question of Cameron, and that the number of those contained in the cyclic group of order
n
is exponential in
n
. For primes
p
, we provide a full characterization of the symmetric complete sum-free subsets of ℤ
p
of size at least (1/3−
c
)·
p
, where
c
> 0 is a universal constant. |
| doi_str_mv | 10.1007/s11856-018-1754-5 |
| format | Article |
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n
is exponential in
n
. For primes
p
, we provide a full characterization of the symmetric complete sum-free subsets of ℤ
p
of size at least (1/3−
c
)·
p
, where
c
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n
is exponential in
n
. For primes
p
, we provide a full characterization of the symmetric complete sum-free subsets of ℤ
p
of size at least (1/3−
c
)·
p
, where
c
> 0 is a universal constant.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Completeness</subject><subject>Group Theory and Generalizations</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Theoretical</subject><issn>0021-2172</issn><issn>1565-8511</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kD1PwzAQhi0EEqXwA9giMRvunJwdj6jiS6rEAMxW6lyqVE0T7GTov8dVkJiY7h2e9z3pEeIW4R4BzENELElLwFKioULSmVggaZIlIZ6LBYBCqdCoS3EV4w6AcoP5QuDHset4DK3PfN8Nex45i1Mnm8Ap8Biz9pD5o98nYBv6aYjX4qKp9pFvfu9SfD0_fa5e5fr95W31uJY-Rz1KLHPd1JbIkrWWalMA-o3V4O0m16pgBZUBNFjVnjGvtCfDYAptVa2Yi3wp7ubdIfTfE8fR7fopHNJLp8AqMkUaThTOlA99jIEbN4S2q8LRIbiTGTebccmMO5lxlDpq7sTEHrYc_pb_L_0AxltkDQ</recordid><startdate>20180801</startdate><enddate>20180801</enddate><creator>Haviv, Ishay</creator><creator>Levy, Dan</creator><general>The Hebrew University Magnes Press</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20180801</creationdate><title>Symmetric complete sum-free sets in cyclic groups</title><author>Haviv, Ishay ; Levy, Dan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-1836fd955959995d7401cb960c9b3624e20a70171adce13a6c57e074692d2ee43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Completeness</topic><topic>Group Theory and Generalizations</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Haviv, Ishay</creatorcontrib><creatorcontrib>Levy, Dan</creatorcontrib><collection>CrossRef</collection><jtitle>Israel journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Haviv, Ishay</au><au>Levy, Dan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Symmetric complete sum-free sets in cyclic groups</atitle><jtitle>Israel journal of mathematics</jtitle><stitle>Isr. J. Math</stitle><date>2018-08-01</date><risdate>2018</risdate><volume>227</volume><issue>2</issue><spage>931</spage><epage>956</epage><pages>931-956</pages><issn>0021-2172</issn><eissn>1565-8511</eissn><abstract>We present constructions of symmetric complete sum-free sets in general finite cyclic groups. It is shown that the relative sizes of the sets are dense in [0, 1/3], answering a question of Cameron, and that the number of those contained in the cyclic group of order
n
is exponential in
n
. For primes
p
, we provide a full characterization of the symmetric complete sum-free subsets of ℤ
p
of size at least (1/3−
c
)·
p
, where
c
> 0 is a universal constant.</abstract><cop>Jerusalem</cop><pub>The Hebrew University Magnes Press</pub><doi>10.1007/s11856-018-1754-5</doi><tpages>26</tpages></addata></record> |
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| ispartof | Israel journal of mathematics, 2018-08, Vol.227 (2), p.931-956 |
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| language | eng |
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| subjects | Algebra Analysis Applications of Mathematics Completeness Group Theory and Generalizations Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical |
| title | Symmetric complete sum-free sets in cyclic groups |
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