On extremal sets without coprimes

• Autorzy: Rudolf Ahlswede , Levon H. Khachatrian
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1994
• Tom: 66
• Numer: 1
• Strony: 89-99

Daty

wydano

1994

otrzymano

1993-05-17

poprawiono

1993-08-24

Twórcy

autor

Rudolf Ahlswede

• Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany

autor

Levon H. Khachatrian

• Institute of Problems of Information and Automation, Armenian Academy of Sciences, 1, P. Sevak St., Erevan 44, Armenia

Bibliografia

• [1] R. Ahlswede and D. E. Daykin, An inequality for the weights of two families of sets, their unions and intersections, Z. Wahrsch. Verw. Gebiete 43 (1978), 183-185.
• [2] R. Ahlswede and D. E. Daykin, The number of values of combinatorial functions, Bull. London Math. Soc. 11 (1979), 49-51.
• [3] R. Ahlswede and D. E. Daykin, Inequalities for a pair of maps S × S → S with S a finite set, Math. Z. 165 (1979), 267-289.
• [4] B. Bollobás, Combinatorics, Cambridge University Press, 1986.
• [5] P. Erdős, On the differences of consecutive primes, Quart. J. Math. Oxford Ser. 6 (1935), 124-128.
• [6] P. Erdős, Remarks in number theory, IV , Mat. Lapok 13 (1962), 228-255.
• [7] P. Erdős, Problems and results on combinatorial number theory, Chapt. 12 in: A Survey of Combinatorial Theory, J. N. Srivastava et al. (eds.), North-Holland, 1973.
• [8] P. Erdős, A survey of problems in combinatorial number theory, Ann. Discrete Math. 6 (1980), 89-115.
• [9] P. Erdős and A. Sárközy, On sets of coprime integers in intervals, preprint No. 9/1992, Mathematical Institute of the Hungarian Academy of Sciences.
• [10] P. Erdős, A. Sárközy and E. Szemerédi, On some extremal properties of sequences of integers, Ann. Univ. Sci. Budapest. Eötvös 12 (1969), 131-135.
• [11] P. Erdős, A. Sárközy and E. Szemerédi, On some extremal properties of sequences of integers, II, Publ. Math. 27 (1980), 117-125.
• [12] J. Marica and J. Schönheim, Differences of sets and a problem of Graham, Canad. Math. Bull. 12 (1969), 635-637.
• [13] R. A. Rankin, The difference between consecutive prime numbers, J. London Math. Soc. 13 (1938), 242-247.
• [14] C. Szabó and G. Tóth, Maximal sequences not containing 4 pairwise coprime integers, Mat. Lapok 32 (1985), 253-257 (in Hungarian).