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A lower bound for the size of a Minkowski sum of dilates

Autor
Hamidoune, Y.O.; Rue, J.
Tipus d'activitat
Article en revista
Revista
Combinatorics probability and computing
Data de publicació
2011-03-01
Volum
20
Número
2
Pàgina inicial
249
Pàgina final
256
DOI
https://doi.org/10.1017/S0963548310000520 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/104404 Obrir en finestra nova
Resum
Let A be a finite non-empty set of integers. An asymptotic estimate of the size of the sum of several dilates was obtained by Bukh. The unique known exact bound concerns the sum |A + k·A|, where k is a prime and |A| is large. In its full generality, this bound is due to Cilleruelo, Serra and the first author. Let k be an odd prime and assume that |A| > 8kk. A corollary to our main result states that |2·A + k·A|=(k+2)|A|-k2-k+2. Notice that |2·P+k·P|=(k+2)|P|-2k, if P is an arithmetic progre...
Citació
Hamidoune, Y.O., Rue, J. A lower bound for the size of a Minkowski sum of dilates. "Combinatorics probability and computing", 1 Març 2011, vol. 20, núm. 2, p. 249-256.
Paraules clau
Minkowski sum
Grup de recerca
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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