Skip to main content
Log in

Euler and combinatorial calculus

  • Conference “Leonhard Euler and Modern Mathematics”
  • Published:
Proceedings of the Steklov Institute of Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. R.C. Bose, S. S. Shrikhande, and E. T. Parker, “Further Results on the Construction of Mutually Orthogonal Latin Squares and the Falsity of Euler’s Conjecture,” Canad. J. Math. 12, 189–203 (1960).

    Article  MathSciNet  MATH  Google Scholar 

  2. R. C. Bose and S. S. Shrikhande, “On the Falsity of Euler’s Conjecture about the Nonexistence of Two Orthogonal Latin Squares of Order 4t + 2,” Proc. Nat. Acad. Sci. USA 45, 734–737 (1959).

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Cauchy, “Recherches sur les polyèdres,” J. École Polytechnique, XVI e Cahier 9, 68–83 (1813).

    Google Scholar 

  4. L. Euler, “Elementa doctrinae solidorum - Demonstratio nonnullaruminsigniumproprietatum, quibus solida hedris planis inclusa sunt praedita,” Novi commentarii Academiae scientiarum imperialis Petropolitanae 4, 109–140 (1752–1753).

    Google Scholar 

  5. L. Euler, “Demonstratio theorematis circa ordinem in summis divisorum observatum,” Novi commentarii Academiae scientiarum imperialis Petropolitanae 5, 75–83 (1760).

    Google Scholar 

  6. L. Euler, “De quadratis magicis,” Mem. Soc. Flessingue, Comm. Arith. Collect. (Éloge St.Petersburg 1783) 2, 593–602 (1849).

    Google Scholar 

  7. L. Euler, “Recherches sur une nouvelle espece de quarres magiques,” Verhandelingen uitgegeven door het Zeeuwsch Genootschap derWetenschappen te Vlissengen 9, 85–239 (1782); Commentationes Arithmeticae 1, 302–361 (1849); in Opera Omnia (Teubner and O. Füssli, Leipzig, 1923), Ser. 1, Vol. 7, pp. 291–392.

    Google Scholar 

  8. L. Euler, “Solutio Problematis ad Geometriam Situs Pertinentis,” Commentarii Academiae Scientiarum Imperialis Petropolitanae 8, 128–140 (1741); in Opera Omnia (Teubner and O. F üssli, Leipzig, 1923), Ser. 1, Vol. 7, pp. 1–10.

    Google Scholar 

  9. L. Euler, “Solution d’une question curieuse que ne paroit soumiseò aucune analyse,” Mémoires de l’Académie des Sciences de Berlin 15(1759), 310–337 (1766); Commentationes Arithmeticae 1, 337–355 (1849); in Opera Omnia (Teubner and O. Füssli, Leipzig, 1923), Ser. 1, Vol. 7, pp. 26–56.

    Google Scholar 

  10. L. Euler, Letters to Scientists (Izd. Akad. Nauk SSSR, Moscow, 1963) [in Russian].

    Google Scholar 

  11. R. A. Fisher, Statistical Methods for Research Workers (Oliver & Boyd, Edinburg, 1925).

    Google Scholar 

  12. R. A. Fisher, “The Arrangement of Field Experiments,” J. Ministry Agriculture 33, 503–513 (1926).

    Google Scholar 

  13. Ch. F. Laywine and G. L. Mullen, Discrete Mathematics Using Latin Squares (Wiley, New York, 1998).

    MATH  Google Scholar 

  14. E. T. Parker, “Orthogonal Latin Squares,” Proc. Nat. Acad. Sci. USA 45, 859–862 (1959).

    Article  MATH  Google Scholar 

  15. H. Poincaré, “Analysis Situs”, J. École Polytechnique, Ser. 2, 1, 1–123 (1895)

    Google Scholar 

  16. G. Tarry, “Le problème des 36 officers”, Compt. Rend. Ser. Math., Astron., Géod. Mécan. 29, 170–203 (1900)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © A.M. Zubkov, 2008, published in Sovremennye Problemy Matematiki, 2008, Vol. 11, pp. 5–18.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zubkov, A.M. Euler and combinatorial calculus. Proc. Steklov Inst. Math. 274 (Suppl 1), 162–168 (2011). https://doi.org/10.1134/S0081543811070030

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0081543811070030

Keywords

Navigation