TY - JOUR
T1 - The polynomial method and restricted sums of congruence classes
AU - Alon, Noga
AU - Nathanson, Melvyn B.
AU - Ruzsa, Imre
N1 - Funding Information:
* E-mail: noga math.tau.ac.il. Research supported in part by a United States Israeli BSF grant and by the Fund for Basic Research administered by the Israel Academy of Sciences. -E-mail: nathansn dimacs.rutgers.edu. Research supported in part by grants from the PSC-CUNY Research Award Program. E-mail: h1140ruz ella.hu. Research supported in part by DIMACS, Rutgers University, and by the Hungarian National Foundation for Scientific Research, Grant 1901.
PY - 1996/2
Y1 - 1996/2
N2 - We present a simple and general algebraic technique for obtaining results in Additive Number Theory, and apply it to derive various new extensions of the Cauchy-Davenport Theorem. In particular we obtain, for subsets A0, A1, ..., Ak of the finite field Zp, a tight lower bound on the minimum possible cardinality of {a0 + a1 + ⋯ + ak: ai∈ Ai, ai ≠ aj for 0 ≤ i < j ≤ k} as a function of the cardinalities of the sets Ai.
AB - We present a simple and general algebraic technique for obtaining results in Additive Number Theory, and apply it to derive various new extensions of the Cauchy-Davenport Theorem. In particular we obtain, for subsets A0, A1, ..., Ak of the finite field Zp, a tight lower bound on the minimum possible cardinality of {a0 + a1 + ⋯ + ak: ai∈ Ai, ai ≠ aj for 0 ≤ i < j ≤ k} as a function of the cardinalities of the sets Ai.
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U2 - 10.1006/jnth.1996.0029
DO - 10.1006/jnth.1996.0029
M3 - Article
AN - SCOPUS:0030079231
SN - 0022-314X
VL - 56
SP - 404
EP - 417
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 2
ER -