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Zap. Nauchn. Sem. POMI, 2016, Volume 448, Pages 135–142 (Mi znsl6308)  

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

J. E. Isomurodovab, K. P. Kokhasa

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.

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English version:
Journal of Mathematical Sciences (New York), 2017, 224:2, 258–262

Bibliographic databases:

UDC: 511.218+519.116
Received: 04.10.2016

Citation: J. E. Isomurodov, K. P. Kokhas, “A set of $12$ numbers is not determined by its set of $4$-sums”, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Zap. Nauchn. Sem. POMI, 448, POMI, St. Petersburg, 2016, 135–142; J. Math. Sci. (N. Y.), 224:2 (2017), 258–262

Citation in format AMSBIB
\Bibitem{IsoKok16}
\by J.~E.~Isomurodov, K.~P.~Kokhas
\paper A set of~$12$ numbers is not determined by its set of $4$-sums
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXVII
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 448
\pages 135--142
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6308}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3576254}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 2
\pages 258--262
\crossref{https://doi.org/10.1007/s10958-017-3411-7}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019751137}


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