DOI: https://doi.org/10.26089/NumMet.v16r452

Composition of infinitary structures

Authors

  • G.G. Ryabov
  • V.A. Serov

Keywords:

n-cube
symbolic matrix
global k-ary tree
k-tuples of natural numbers
difference tabloid
symmetry of prime numbers
incompatibility relation

Abstract

The infinitary structure of an n-cube, global k-ary trees, and natural numbers are considered as a single genetic structure. A number of geometric characteristics of the shortest paths in an n-cube are specified and the properties of prime number symmetry among the natural numbers are studied on the basis of this structure.

New computational technologies

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Published

2015-09-30

Issue

Vol. 16 (2015): Issue 4.

Section

Section 1. Numerical methods and applications

Author Biographies

G.G. Ryabov

Lomonosov Moscow State University,
Research Computing Center
• Head of Laboratory

V.A. Serov

Lomonosov Moscow State University,
Research Computing Center
• Researcher

References

  1. J. Pintz, Patterns of Primes in Arithmetic Progressions , arXiv preprint: 1509.01564v2 [math.NT] (Cornell Univ. Library, Ithaca, 2015), available at
    http://arxiv.org/abs/1509.01564.
  2. K. Ford, B. Green, S. Konyagin, et al., Long Gaps between Primes , arXiv preprint: 1412.5029v2 [math.NT] (Cornell Univ. Library, Ithaca, 2015), available at
    http://arxiv.org/abs/1412.5029.
  3. D. H. J. Polymath, Variants of the Selberg Sieve, and Bounded Intervals Containing Many Primes , arXiv preprint: 1407.4897v4 [math.NT] (Cornell Univ. Library, Ithaca, 2014),
    available at
    http://arxiv.org/abs/1407.4897.
  4. G. G. Ryabov, “On the Quaternary Coding of Cubic Structures,” Vychisl. Metody Programm. 10, 340-347 (2009).
  5. G. G. Ryabov, “Hausdorff Metric on Faces of the n-Cube,” Fundam. Prikl. Mat. 16 (1), 151-155 (2010) [J. Math. Sci. 177 (4), 619-622 (2011)].
  6. G. G. Ryabov and V. A. Serov, “Multidimensional Metro and Symbol Matrices,” Int. J. Open Inform. Technol. 2 (11), 10-18 (2014).
    http://injoit.org/index.php/j1/article/view/157/116 . Cited November 6, 2015.
  7. G. Ryabov and V. Serov, “On Classification of k-Dimension Paths in n-Cube,” App. Math. 5 (4), 723-727 (2014).
    doi 10.4236/am.2014.54069
  8. G. G. Ryabov and V. A. Serov, “Polymorphism of Symbolic Ternary Matrices and Genetic Space of the Shortest k-Paths in the n-Cube,” Int. J. Open Inform. Technol. 3 (7), 1-11 (2015).
    http://injoit.org/index.php/j1/article/view/214/173 . Cited November 6, 2015.