Have a personal or library account? Click to login

Quasi-Random Graphs, Pseudo-Random Graphs and Pseudorandom Binary Sequences, I. (Quasi-Random Graphs)

Uniform distribution theory
Volume 14 (2019): Issue 2 (December 2019)
By:
Open Access
|Mar 2020

References

  1. [1] ALON, N.—KOHAYAKAWA, Y.— MAUDUIT, C.—MOREIRA, C. G.—RÖDL, V.: Measures of pseudorandomness for finite sequences: minimal values, Comb. Probab. Comput. 15 (2006), 1–29.10.1017/S0963548305007170
    Search in Google ScholarBack to article
  2. [2] –––––– Measures of pseudorandomness for finite sequences: typical values, Proc. London Math. Soc. 95 (2007), 778–812.10.1112/plms/pdm027
    Search in Google ScholarBack to article
  3. [3] BOLLOBÁS, B.: Random Graphs. Academic Press, London, 1985.
    Search in Google ScholarBack to article
  4. [4] CASSAIGNE, J.—MAUDUIT, C.—SÁRKÖZY, A.: On finite pseudorandom binary sequences VII: The measures of pseudorandomness,Acta Arith. 103 (2002), 97–118.10.4064/aa103-2-1
    Search in Google ScholarBack to article
  5. [5] CHUNG, F. R. K.—GRAHAM, R. L.—WILSON, R. M.: Quasirandom graphs,Proc. Nat. Acad. Sci. U.S.A., 85 (1988), 969–970.10.1073/pnas.85.4.96927968116593909
    Search in Google ScholarBack to article
  6. [6] –––––– Quasirandom graphs, Combinatorica 9 (1989), 345–362.10.1007/BF02125347
    Search in Google ScholarBack to article
  7. [7] DAVIS, P. J.: Circulant Matrices. Wiley, New York, 1970.
    Search in Google ScholarBack to article
  8. [8] GOUBIN, L.—MAUDUIT, C.—SÁRKÖZY, A.: Construction of large families of pseudorandom binary sequences, J. Number Theory 106 (2004), 56–69.10.1016/j.jnt.2003.12.002
    Search in Google ScholarBack to article
  9. [9] GYARMATI, K.: On a family of pseudorandom binary sequences, Period. Math. Hungar. 49 (2004), 45–63.10.1007/s10998-004-0522-y
    Search in Google ScholarBack to article
  10. [10] –––––– On a fast version of a pseudorandom generator.In: General Theory of Information Transfer and Combinatorics. (R. Ahlswede et al.,eds.) In: Lecture Notes Comput. Sci. Vol. 4123, Springer, Berlin, 2006, pp. 326–342.10.1007/11889342_18
    Search in Google ScholarBack to article
  11. [11] –––––– Measures of pseudorandomness.In: Finite Fields and Their Applications, Character Sums and Polynomials (P. Charpin et al., eds.) In: Radon Series on Comput. Appl. Math.Vol.11, De Gruyter, Berlin, 2013, pp. 43–64.10.1515/9783110283600.43
    Search in Google ScholarBack to article
  12. [12] GYARMATI, K.—MAUDUIT, C.—SÁRKÖZY, A.:, Generation of further pseudorandom binary sequences, I (Blowing up a single sequence), Unif. Distrib. Theory 10 (2015), 35–61.
    Search in Google ScholarBack to article
  13. [13] LIU, H.:, Large families of pseudorandom binary sequences and lattices by using the multiplicative inverse,Acta Arith. 159 (2013), 123–131.10.4064/aa159-2-3
    Search in Google ScholarBack to article
  14. [14] LIU, H. N.—ZHAN, T.—WANG, X. Y.: On the correlation of pseudorandom binary sequences with composite moduli, Publ. Math. Debrecen 74 (2009), 195–214.10.5486/PMD.2009.4368
    Search in Google ScholarBack to article
  15. [15] MAUDUIT, C.—RIVAT, J.—SÁRKÖZY, A.: Construction of pseudorandom binary sequences using additive characters, Monatshefte Math. 141 (2004), 197–208.10.1007/s00605-003-0112-8
    Search in Google ScholarBack to article
  16. [16] MAUDUIT, C.—SÁRKÖZY, A.: On finite pseudorandom binary sequences, I: Measure of pseudorandomness, the Legendre symbol,Acta Arith. 82 (1997), 365–377.10.4064/aa-82-4-365-377
    Search in Google ScholarBack to article
  17. [17] –––––– Construction of pseudorandom binary sequences by using the multiplicative inverse, Acta Math. Hungar. 108 (2005), 239–252.10.1007/s10474-005-0222-y
    Search in Google ScholarBack to article
  18. [18] RIVAT, J.—SÁRKÖZY, A.: Modular constructions of pseudorandom binary sequences with composite moduli, Periodica Math. Hungar. 51 (2005), 75–107.10.1007/s10998-005-0031-7
    Search in Google ScholarBack to article
  19. [19] SÁRKÖZY, A.: A finite pseudorandom binary sequence, Studia Sci. Math. Hungar. 38 (2001), 17–35.10.1556/sscmath.38.2001.1-4.28
    Search in Google ScholarBack to article
  20. [20] –––––– On finite pseudorandom binary sequences and their applications in cryptography, Tatra Mt. Math. Publ. 37 (2007), 123–136.
    Search in Google ScholarBack to article
  21. [21] THOMASON, A.: Pseudorandom graphs, In: Random Graphs’85, Poznań 1985 (M. Karonski, ed.), In: North-Holland Math. Stud. Vol. 144.In: Ann. Discrete Math. Vol. 33, North-Holland, Amsterdam, 1987. pp. 307–33.10.1016/S0304-0208(08)73063-9
    Search in Google ScholarBack to article
  22. [22] –––––– Random graphs, strongly regular graphs and pseudo-random graphs,In: Surveys in Combinatorics 1987 (C. Whitehead, ed.). In: London Mat. Soc. Lecture Notes Series Vol. 123, Cambridge Univ. Press, Cambridge, 1987, pp. 173–196.
    Search in Google ScholarBack to article
  23. [23] VILFRED, V.: On circulant graphs,In: Graph Theory and its Applications (R. Balakrishnan et al., eds.), (Anna University, Chennai, March 14–16, 2001) Alpha Science, pp. 34–36.
    Search in Google ScholarBack to article
  24. [24] WEIL, A.: Sur les curbes algébriques et les variétés qui s’en déduisent, Acta Sci. Ind. 1041, Hermann, Paris, 1948.
    Search in Google ScholarBack to article
DOI: https://doi.org/10.2478/udt-2019-0017 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X
Journal RSS Feed
Language: English
Page range: 103 - 126
Submitted on: Jul 8, 2019
Accepted on: Oct 25, 2019
Published on: Mar 27, 2020
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
Keywords:
quasi-random graph,
pseudo-random graph,
pseudorandom binary sequence. Research partially supported by Hungarian National Research Development and Innovation Fund K119528
Related subjects:
Mathematics,
Algebra and number theory,
Discrete mathematics,
Probability and statistics,
Numerical and computational mathematics

© 2020 József Borbély, András Sárközy, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Previous articleVolume 14 (2019): Issue 2 (December 2019)