A Complete Annotated Bibliography of Work Related to Sidon Sequences

A Sidon sequence is a sequence of integers $a_1 < a_2 < \cdots$ with the property that the sums $a_i + a_j$ $(i\le j)$ are distinct. This work contains a survey of Sidon sequences and their generalizations, and an extensive annotated and hyperlinked bibliography of related work.

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

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

[3]  R. C. Bose.  An Affine Analogue of Singer's Theorem , 1942 .

[4]  P. Erdös.  On a Problem of Sidon in Additive Number Theory and on Some Related Problems Addendum , 1944 .

[5]  A. Stöhr,et al.  Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe. II. , 1955 .

[6]  A. Stöhr,et al.  Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe. I. , 1955 .

[7]  Paul Erdös,et al.  Additive properties of random sequences of positive integers , 1960 .

[8]  Fritz Krückeberg.  B2-Folgen und verwandte Zahlenfolgen. , 1961 .

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

[10]  H. Halberstam,et al.  ON PERFECT DIFFERENCE SETS , 1963 .

[11]  B. Lindström.  Determination of two vectors from the sum , 1969 .

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

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

[14]  B. Lindström.  On B2-sequences of vectors , 1972 .

[15]  Endre Szemerédi,et al.  Linear problems in combinatorial number theory , 1975 .

[16]  N. J. A. Sloane,et al.  On Additive Bases and Harmonious Graphs , 1980, SIAM J. Algebraic Discret. Methods.

[17]  Paul Erdös.  Some Applications of Ramsey's Theorem to Additive Number Theory , 1980, Eur. J. Comb..

[18]  János Komlós,et al.  A Dense Infinite Sidon Sequence , 1981, Eur. J. Comb..

[19]  R. Guy.  Unsolved Problems in Number Theory , 1981 .

[20]  P. Erdös.  Some of My Favourite Problems Which Recently have Been Solved , 1982 .

[21]  Ronald L. Rivest,et al.  A Knapsack Type Public Key Cryptosystem Based On Arithmetic in Finite Fields , 1984, CRYPTO.

[22]  A. D'yachkov,et al.  Bs-sequences , 1984 .

[23]  P. Erdös,et al.  On Disjoint Sets of Differences , 1984 .

[24]  László Babai,et al.  Sidon Sets in Groups and Induced Subgraphs of Cayley Graphs , 1985, Eur. J. Comb..

[25]  P. Erdös.  Some Applications of Probability Methods to Number Theory , 1985 .

[26]  Noga Alon,et al.  An Application of Graph Theory to Additive Number Theory , 1985, Eur. J. Comb..

[27]  András Sárközy,et al.  Problems and results on additive properties of general sequences. I. , 1985 .

[28]  P. ERDs.  Problems and Results on Additive Properties of General Sequences , 1986 .

[29]  Andrew D. Pollington.  On the density of B2-bases , 1986, Discret. Math..

[30]  D. Hajela,et al.  Some remarks on Bh[g] sequences , 1988 .

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

[32]  P. Erdos.  Some old and new problems on additive and combinatorial number theory , 1989 .

[33]  H. L. Abbott,et al.  Sidon Sets , 1990, Canadian Mathematical Bulletin.

[34]  J. Cilleruelo.  $B_{2}$-sequences whose terms are squares , 1990 .

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

[36]  P. Korman.  An Upper Bound , 1991, SIAM Rev..

[37]  Enrico Bombieri,et al.  Squares in arithmetic progressions , 1992 .

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

[39]  A ₂-sequence with larger reciprocal sum , 1993 .

[40]  Imre Z. Ruzsa,et al.  Solving a linear equation in a set of integers I , 1993 .

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

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

[43]  Paul Erdös,et al.  On additive properties of general sequences , 1994, Discret. Math..

[44]  A. Sarkozy,et al.  On Sum Sets of Sidon Sets, 1. , 1994 .

[45]  Zhenxiang Zhang,et al.  Finding finite B2-sequences with larger m-am1/2 , 1994 .

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

[47]  Mihail N. Kolountzakis,et al.  An effective additive basis for the integers , 1995, SODA '94.

[48]  M. Helm.  A Remark on B2k-Sequences , 1994 .

[49]  Hanno Lefmann,et al.  Point sets with distinct distances , 1995, Comb..

[50]  Claus-Peter Schnorr,et al.  Attacking the Chor-Rivest Cryptosystem by Improved Lattice Reduction , 1995, EUROCRYPT.

[51]  J. Spencer,et al.  SIDON SETS WITH SMALL GAPS , 1995 .

[52]  B2[g] sequences whose terms are squares , 1995 .

[53]  András Sárközy,et al.  On sum sets of sidon sets, II , 1995 .

[54]  Mihail N. Kolountzakis,et al.  The Density ofBh[g] Sequences and the Minimum of Dense Cosine Sums , 1996 .

[55]  András Sárközy,et al.  Combinatorial number theory , 1996 .

[56]  Xingde Jia.  Bh[g]-Sequences with Large Upper Density , 1996 .

[57]  Imre Z. Ruzsa,et al.  Sumsets of Sidon sets , 1996 .

[58]  Béla Bajnok.  Constructions of Spherical 3-Designs , 1998, Graphs Comb..

[59]  Imre Z. Ruzsa,et al.  An Infinite Sidon Sequence , 1998 .

[60]  Bernt Lindström,et al.  Well Distribution of Sidon Sets in Residue Classes , 1998 .

[61]  Mihail N. Kolountzakis,et al.  On the Uniform Distribution in Residue Classes of Dense Sets of Integers with Distinct Sums , 1998 .

[62]  Anand Srivastav,et al.  Probabilistic Construction of Small Strongly Sum-Free Sets via Large Sidon Sets , 1999, RANDOM-APPROX.

[63]  Paul Erdös,et al.  Notes on Sum-Free and Related Sets , 1999 .

[64]  Svante Janson,et al.  Random Sidon Sequences , 1999 .

[65]  A TRANSLATE OF BOSE –CHOWLA B 2 -SETS , 2000 .

[66]  Javier Cilleruelo.  An Upper Bound for B2[2] Sequences , 2000, J. Comb. Theory, Ser. A.

[67]  M. Nathanson.  N-graphs, Modular Sidon and Sum-Free Sets, and Partition Identities , 2000, math/0002173.

[68]  Oriol Serra,et al.  On a generalization of a theorem by Vosper. , 2000 .

[69]  Probabilistic construction of small strongly sum-free sets via large Sidon sets , 2000 .

[70]  G. Yovanof,et al.  B2-sequences and the distinct distance constant , 2000 .

[71]  I. Ruzsa.  AN ALMOST POLYNOMIAL SIDON SEQUENCE , 2001 .

[72]  Alan C. H. Ling,et al.  Slope packings and coverings, and generic algorithms for the discrete logarithm problem , 2001, IACR Cryptol. ePrint Arch..

[73]  B. Green.  The number of squares and $B_h[g]$ sets , 2001 .

[74]  Gérard D. Cohen,et al.  Binary B2-Sequences : A New Upper Bound , 2001, J. Comb. Theory, Ser. A.

[75]  P. Ebdos,et al.  ON A PROBLEM OF SIDON IN ADDITIVE NUMBER THEORY, AND ON SOME RELATED PROBLEMS , 2002 .

[76]  J. Cilleruelo,et al.  Upper and Lower Bounds for Finite Bh[g] Sequences , 2002 .

[77]  The distribution of dense Sidon subsets of $ \mathbb{Z}_m $ , 2002 .

[78]  David R. Wood,et al.  On vertex-magic and edge-magic total injections of graphs , 2002, Australas. J Comb..

[79]  Kevin O'Bryant,et al.  Continuous Ramsey Theory and Sidon Sets , 2002 .

[80]  Hendrik W. Lenstra.  On the Chor—Rivest knapsack cryptosystem , 2004, Journal of Cryptology.

[81]  Sequences , 2005 .

[82]  Béla Bollobás,et al.  Integer sets with prescribed pairwise differences being distinct , 2005, Eur. J. Comb..

[83]  Oleg Pikhurko.  Dense edge-magic graphs and thin additive bases , 2006, Discret. Math..

[84]  B. Lindström.  PRIMITIVE QUADRATICS REFLECTED IN B2-SEQUENCES , 2022 .

[85]  P. Erdos,et al.  On sparse sets hitting linear forms , 2022 .