论文信息 - B h sequences

B h sequences

Let A be a set (finite or infinite) of natural numbers, and let a i denote a generic element of A. We say that A is a B h sequence if the sums of the form a 1 + … + a h (a 1 ≤ … ≤ a h ) are all distinct. We give an expository account of upper bounds for B h sequences. We also give a new upper bound for B 3 sequences.

S. W. Graham

[1] Sheng’an Chen,et al. On Sidon sequences of even orders , 1993 .

[2] J. Nash. On B 4-Sequences , 1989, Canadian Mathematical Bulletin.

[3] B. Linström,et al. An inequality for B2-sequences , 1969 .

[4] Xingde Jia,et al. On Finite Sidon Sequences , 1993 .

[5] Sheng’an Chen,et al. On the size of finite Sidon sequences , 1994 .

[6] B. Lindström. A remark on B4-Sequences , 1969 .

[7] Grigori Kolesnik,et al. Van der Corput's method of exponential sums , 1991 .

[8] Xingde Jia. On B2k-Sequences , 1994 .

[9] Paul Erdős,et al. On sums of a Sidon-sequence , 1991 .

[10] P. Erdös,et al. On a problem of sidon in additive number theory, and on some related problems , 1941 .

[11] J. Singer. A theorem in finite projective geometry and some applications to number theory , 1938 .

[12] R. C. Bose,et al. Theorems in the additive theory of numbers , 1962 .

[13] S. Sidon. Ein Satz über trigonometrische Polynome und seine Anwendung in der Theorie der Fourier-Reihen , 1932 .