J. E. Isomurodov, K. P. Kokhas, “A set of $12$ numbers is not determined by its set of $4$-sums”, Zap. Nauchn. Sem. POMI, 2016, Volume 448,Pages 135

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A set of $12$ numbers is not determined by its set of $4$-sums

J. E. Isomurodov^ab, K. P. Kokhas^a

^a St. Petersburg State University, St. Petersburg, Russia
^b St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia

Abstract: 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.

Key words and phrases: additive combinatorics, sums sets.

UDC: 511.218+519.116

Received: 04.10.2016