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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 448, Pages 135–142 (Mi znsl6308)  
This article is cited in 1 scientific paper (total in 1 paper)

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
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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.
Received: 04.10.2016
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 224, Issue 2, Pages 258–262
DOI: https://doi.org/10.1007/s10958-017-3411-7
Bibliographic databases:
Document Type: Article
UDC: 511.218+519.116
Language: Russian
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://mathscinet.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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019751137}
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  • https://www.mathnet.ru/eng/znsl/v448/p135
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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