Geodesic
Some generalizations of the Cauchy--Davenport theorem
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIV, Tome 432 (2015), pp. 105-110

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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. 
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     author = {V. V. Volkov and F. V. Petrov},
     title = {Some generalizations of the {Cauchy--Davenport} theorem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_432_a6/}
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V. V. Volkov; F. V. Petrov. Some generalizations of the Cauchy--Davenport theorem. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIV, Tome 432 (2015), pp. 105-110. http://geodesic.mathdoc.fr/item/ZNSL_2015_432_a6/