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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 432, Pages 105–110 (Mi znsl6113)  

Some generalizations of the Cauchy–Davenport theorem

V. V. Volkova, F. V. Petrovab

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
References:
Abstract: We investigate two possible generalizations of the Cauchy–Davenport inequality $|A+B|\geq\min(p,|A|+|B|-1)$ for nonempty sets $A,B$ of residues modulo a prime number $p$. The first one deals with another way of measuring the size of a set of points in an affine space (rather than just taking the cardinality), namely, with algebraic complexity. The second one concentrates on the multiplicative group of a field.
Key words and phrases: Cauchy–Davenport inequality, polynomial method, algebraic complexity.
Received: 26.01.2015
English version:
Journal of Mathematical Sciences (New York), 2015, Volume 209, Issue 6, Pages 874–877
DOI: https://doi.org/10.1007/s10958-015-2534-y
Bibliographic databases:
Document Type: Article
UDC: 519.118+512.622
Language: Russian
Citation: V. V. Volkov, F. V. Petrov, “Some generalizations of the Cauchy–Davenport theorem”, Representation theory, dynamical systems, combinatorial methods. Part XXIV, Zap. Nauchn. Sem. POMI, 432, POMI, St. Petersburg, 2015, 105–110; J. Math. Sci. (N. Y.), 209:6 (2015), 874–877
Citation in format AMSBIB
\Bibitem{VolPet15}
\by V.~V.~Volkov, F.~V.~Petrov
\paper Some generalizations of the Cauchy--Davenport theorem
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXIV
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 432
\pages 105--110
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6113}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 209
\issue 6
\pages 874--877
\crossref{https://doi.org/10.1007/s10958-015-2534-y}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84939421233}
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  • https://www.mathnet.ru/eng/znsl6113
  • https://www.mathnet.ru/eng/znsl/v432/p105
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