The 3 x + 1 problem, generalized Pascal triangles and cellular automata

Ivan Korec

Mathematica Slovaca (1992)

  • Volume: 42, Issue: 5, page 547-563
  • ISSN: 0232-0525

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Korec, Ivan. "The $3x+1$ problem, generalized Pascal triangles and cellular automata." Mathematica Slovaca 42.5 (1992): 547-563. <http://eudml.org/doc/32424>.

@article{Korec1992,
author = {Korec, Ivan},
journal = {Mathematica Slovaca},
keywords = {Collatz function; -conjecture; generalized Pascal triangles; cellular automata},
language = {eng},
number = {5},
pages = {547-563},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {The $3x+1$ problem, generalized Pascal triangles and cellular automata},
url = {http://eudml.org/doc/32424},
volume = {42},
year = {1992},
}

TY - JOUR
AU - Korec, Ivan
TI - The $3x+1$ problem, generalized Pascal triangles and cellular automata
JO - Mathematica Slovaca
PY - 1992
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 42
IS - 5
SP - 547
EP - 563
LA - eng
KW - Collatz function; -conjecture; generalized Pascal triangles; cellular automata
UR - http://eudml.org/doc/32424
ER -

References

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  1. CLONEY T., GOLES C. E., VICHNIAC G. Y., The 3x + 1 problem: A quasi-cellular automaton, Complex Systems 1 (1987), 349-360. (1987) Zbl0662.10010MR0891956
  2. CULIK H. K., GRUSKA J., SALOMAA A., Systolic trellis automata, Internat. J. Comput. Math. 15 and 16 (1984), 195 -212 and 3-22. (1984) Zbl0571.68042MR0754266
  3. CULIK H. K., HURD L. P., YU S., Computation theoretic aspects of cellular automata, Phys. D 45 (1990), 357-378. (1990) Zbl0729.68052MR1094881
  4. KOREC I., Generalized Pascal triangles, Decidability results, Acta Math. Univ. Comen. XLVI-XLVII (1985), 93-130. (1985) Zbl0607.05002MR0872334
  5. KOREC I., Generalized Pascal triangles, (Slovak), DrSc. Thesis, UK Bratislava. 1984. (1984) 
  6. KOREC I., Generalized Pascal triangles, In: Proceedings of the V Universal Algebra Symposium, Turawa, Poland, May 1988 (K. Halkowska and S. Stawski, eds.), World Scientific, Singapore, 1989, pp. 198-218. (1988) MR1084405
  7. KUIPERS L. NIEDERREITEIR H., Uniform distribution of sequences, J. Wiley & Sons, New York, 1974. (1974) MR0419394
  8. LAGARIAS J. C., The 3x + 1 problem and its generalizations, Amer. Math. Monthly 92 (1985), 3-23. (1985) Zbl0566.10007MR0777565
  9. WOLFRAM S., Computation theory of cellular automata, Comm. Math. Phys. 96 (1984), 15-57. (1984) Zbl0587.68050MR0765959

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