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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 432, Pages 105–110
(Mi znsl6113)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/znsl6113 https://www.mathnet.ru/eng/znsl/v432/p105
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Abstract page: | 338 | Full-text PDF : | 131 | References: | 39 |
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