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Bh [g] sequences

  • Javier Cilleruelo (a1) and Jorge Jiménez-Urroz (a2)


New upper and lower bounds are given for Fh(g, N), the maximum size of a Bh[g] sequence contained in [1, N]. It is proved that and that

and that, for any ε > 0 and g > g(ε, h),



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[B-Ch]Bose, R. C. and Chowla, S.. Theorems in the additive theory of numbers. Comment. Math. Helv., 37 (1962/1963), 141147.
[C-R-T]Cilleruelo, J., Ruzsa, I. and Trujillo, C.. Upper and lower bounds for Bh[g] sequences. J. Number Theory (to appear).
[Cl]Cilleruelo, J.. New upper bounds for finite Bh sequences. Advances Math. 159 (2001), 117.
[C2]Cilleruelo, J.. An upper bound for B2[2] sequences. J. Combinat. Theory A, 89 (2000), 141144.
[E-T]Erdős, P. and Turan, P.. On a problem of Sidon in additive number theory and on some related problems. J. London Math. Soc., 16 (1941), 212215; Addendum (by P. Erdős), J. London Math. Soc., 19 (1944), 208.
[H-R]Halberstam, H. and Roth, K. F.. Sequences (Springer-Verlag, New York, 1983).
[H]Helm, M.. Upper bounds for B2[g]-sets (preprint).
[K]Kolountzakis, M.. Problems in the Additive Number Theory of General Sets, I. Sets with distinct sums. (1996, Available at
[L-N]Lesieur, L. and Nicolas, J. L.. On the Eulerian numbers Mn = max1≤knA(n, k). Europ. J. Comb., 13 (1992), 379399.
[L]Lindstrom, B.. B2[g]-sequences from Bh sequences. Proc. Amer. Math. Soc., 128 (2000), 657659.
[N]Nicolas, J. L.. An integral representation for Eulerian numbers. Coll. Math. Soc. Jdnos Bolyai 60: Sets, Graphs and Numbers (Budapest, 1991),
[R]Ruzsa, I.. Solving a linear equation I. Acta Arithmetica LXV.3 (1993).
[S-S]Sarkozy, A. and Sos, V. T.. The Mathematics of Paul Erdős, vol. I: Algorithms and Combinatorics, 13 (Springer, 1996).
[S]Singer, J.. A theorem in finite projective geometry and some applications to number theory. Trans. Amer. Math. Soc., 43 (1938), 377385.
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