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Number Theory » Combinatorial N.T.

Snevily's conjecture ★★★

Author(s): Snevily

Conjecture   Let $ G $ be an abelian group of odd order and let $ A,B \subseteq G $ satisfy $ |A| = |B| = k $. Then the elements of $ A $ and $ B $ may be ordered $ A = \{a_1,\ldots,a_k\} $ and $ B = \{b_1,\ldots,b_k\} $ so that the sums $ a_1+b_1, a_2+b_2 \ldots, a_k + b_k $ are pairwise distinct.

Keywords: addition table; latin square; transversal

Posted by mdevos
updated May 27th, 2011
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