鎖の形と数の定和性に関する問題

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  • A Problem Concerning a Chain of m Circles with a Property of Constant Sum

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Let us consider a problem concerning a chain of m circles with a property of constant sum; indeed, we are requested to seek a permutation ･･･ of 2m integers {0,1,2,…,2m-1} which satisfies the following condition : (1) a0+a1+a2 = a2+a3+a4 =…=a2m-2+a2m-1+a0. Behind such a problem in combinatorial mathematics, there exists an interesting graph structure, and in the cases of 3 ≦ m ≦ 7, the author was successful in listing up all solutions (a1) with constant sum (1). In addition, he discusses related problems from a viewpoint of random permutations.

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