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Problems

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Part of the book series: Developments in Mathematics ((DEVM,volume 57))

Abstract

In the 1992 book, “Orthomorphism graphs of groups”, we gave a list of 74 problems. Some of these have since been solved. In this chapter we will reorganize, update, and amend this list of problems and will include many additional problems.

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References

  1. Colbourn, C.J., Dinitz, J.H., Wanless, I.M.: Latin squares. In: Colbourn, C.J., Dinitz, J.H. (eds) Handbook of Combinatorial Designs, 2nd. edn., pp. 135–160. Chapman & Hall/CRC, Florida (2007)

    Google Scholar 

  2. Dénes, J., Keedwell, A.D.: Latin Squares and Their Applications. English Universities Press, London (1974)

    MATH  Google Scholar 

  3. Dénes, J., Keedwell, A.D.: Latin Squares and Their Applications, 2nd. edn. North Holland, Amsterdam (2015)

    MATH  Google Scholar 

  4. Dinitz, J.H., Stinson, D.R.: Room squares and related designs, in: Dinitz, J.H., Stinson, D.R. (eds.) Contemporary design theory: a collection of surveys, pp. 137–204. John Wiley & Sons, New York (1992)

    MATH  Google Scholar 

  5. Evans, A.B.: Orthomorphism graphs of groups. Lecture Notes in Mathematics 1535, Springer-Verlag, Berlin (1992)

    Google Scholar 

  6. Evans, A.B.: The existence of strong complete mappings. Electron. J. Combin. 19, # P34 (2012)

    Google Scholar 

  7. Evans, A.B., Narayan, D.A.. Urick, J.: Representations of graphs modulo n: Some problems. Bull. Inst. Combin. Appl. 56, 85–97 (2009)

    MathSciNet  MATH  Google Scholar 

  8. Fear, D., Wanless, I.M.: Existence results for cyclotomic orthomorphisms. J. Algebraic Combin. 46, 1–14 (2017).

    Article  MathSciNet  Google Scholar 

  9. Grüttmüller, M.: Completing partial Latin squares with prescribed diagonals. Discrete Appl. Math. 138, 89–97 (2004)

    Article  MathSciNet  Google Scholar 

  10. Jungnickel, D.: Lateinsche Quadrate, ihre Geometrien und ihre Gruppen. Jahresber. Dtsch Math.-Ver. 86, 69–108 (1984)

    MATH  Google Scholar 

  11. Jungnickel, D.: Latin squares, their geometries and their groups. A survey. In: Coding Theory and design Theory, part II, pp. 166–225. IMA Vol. Math. Appl. 21. Springer-Verlag, New York (1990)

    Google Scholar 

  12. Keedwell, A.D.: Sequenceable groups, generalized complete mappings, neofields and block designs. In: Combinatorial Mathematics X (Adelaide, 1982), pp. 49–71. Lecture Notes in Math. 1036. Springer, Berlin (1983)

    Google Scholar 

  13. McKay, B.D., McLeod, J.C., Wanless, I.M.: The number of transversals in a Latin square. Des. Codes Crytogr. 40, 269–284 (2006)

    Article  MathSciNet  Google Scholar 

  14. Shieh, Y.-P., Hsiang, J., Hsu, D.F.: On the existence problems of complete mappings. Preprint.

    Google Scholar 

  15. Wanless, I.M.: Atomic Latin squares based on cyclotomic orthomorphisms. Electron. J. Combin. 12, R22 (2005)

    MathSciNet  MATH  Google Scholar 

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Evans, A.B. (2018). Problems. In: Orthogonal Latin Squares Based on Groups. Developments in Mathematics, vol 57. Springer, Cham. https://doi.org/10.1007/978-3-319-94430-2_16

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