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A140794
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The smallest counterexample to the conjecture that the cardinality of the sumset is less than or equal to the cardinality of the difference set of every finite set of integers.
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0
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OFFSET
| 1,2
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COMMENTS
| A set with more sums than differences is called a MSTD set. Hegarty has constructed many such examples. Nathanson's abstract: This is a survey of open problems in different parts of combinatorial and additive number theory.
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REFERENCES
| P. V. Hegarty, Some explicit constructions of sets with more sums than differences, Acta Arith. 130(2007)61-77.
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LINKS
| Melvyn B. Nathanson, Problems in Additive Number Theory, III: Thematic Seminars at the Centre de Recerca Matematica, arXiv:0807.2073
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EXAMPLE
| Let A = {0, 2, 4, 7, 11, 12, 14}. Then the cardinality of the sumset, |A + A| = 26, while the cardinality of the difference set, |A - A| = 25.
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CROSSREFS
| Sequence in context: A134126 A091263 A101430 * A127575 A206853 A106265
Adjacent sequences: A140791 A140792 A140793 * A140795 A140796 A140797
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KEYWORD
| fini,full,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 15 2008
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