Geodesic
A set of $12$ numbers is not determined by its set of $4$-sums
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 135-142
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We present two sets of $12$ integers that have the same sets of $4$-sums. The proof of the uniqueness of determination of a set of $12$ numbers by its set of $4$-sums published 50 years ago is wrong, and we demonstrate an incorrect calculation in it. 
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J. E. Isomurodov; K. P. Kokhas. A set of $12$ numbers is not determined by its set of $4$-sums. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 135-142. http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a8/

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