Compound orthomorphisms of the cyclic group

Finite Fields and their Applications

Volumn 16, Issue 4, 2010, Pages 277-289

  Stones, Douglas S ^a   Wanless, Ian M ^a  

^a MONASH UNIVERSITY   (Australia)

Author keywords

Compatible orthomorphism; Compound orthomorphism; Latin square; Orthomorphism; Partial orthomorphism; Polynomial orthomorphism

Indexed keywords

ALGEBRA; FINITE ELEMENT METHOD;

COMPATIBLE ORTHOMORPHISM; COMPOUND ORTHOMORPHISM; LATIN SQUARE; ORTHOMORPHISM; PARTIAL ORTHOMORPHISM;

POLYNOMIALS;

EID: 77955685994     PISSN: 10715797     EISSN: 10902465     Source Type: Journal    
DOI: 10.1016/j.ffa.2010.04.001     Document Type: Article

References (30)

1. G.K. Bennett, M.J. Grannell, T.S. Griggs, Exponential lower bounds for the numbers of Skolem-type sequences, Ars Combin. 73 (2004) 101-106. (Pubitemid 41453414)
2. W. Bosma, Cubic reciprocity explicit primality tests for h · 3k ± 1, in: High Primes and Misdemeanours, in: Fields Inst. Commun., vol. 41, Amer. Math. Soc., 2004, pp. 77-89.
3. N.J. Cavenagh, C. Hämäläinen, A.M. Nelson, On completing three cyclically generated transversals to a Latin square, Finite Fields Appl. 15 (2009) 294-303.
4. N.J. Cavenagh, I.M. Wanless, On the number of transversals in Cayley tables of cyclic groups, Discrete Appl. Math. 158 (2010) 136-146.
5. D. Clark, J.T. Lewis, Transversals of cyclic Latin squares, Congr. Numer. 128 (1997) 113-120.
6. C. Cooper, A lower bound for the number of good permutations, Data Recording Storage Process. (Nat. Acad. Sci. Ukraine) 2 (2000) 15-25.
7. C. Cooper, R. Gilchrist, I.N. Kovalenko, D. Novakovic, Estimation of the number of "good" permutations, with applications to cryptography, Cybernet. Systems Anal. 35 (2000) 688-693.
8. C. Cooper, I.N. Kovalenko, An upper bound on the number of complete mappings, Theory Probab. Math. Statist. 53 (1995) 77-83.
9. L. Euler, Recherches sur une nouvelle espéce de quarrés magiques, Verh. Zeeuwsch. Gennot. Weten. Vliss. 9 (1782) 85-239, Eneström E530, Opera Omnia OI7, 291-392.
10. A.B. Evans, Orthomorphism Graphs of Groups, Springer, 1992.
11. A.B. Evans, On orthogonal orthomorphisms of cyclic and non-abelian groups. II, J. Combin. Des. 15 (2007) 195-209. (Pubitemid 46721617)
12. M. Grüttmüller, Completing partial Latin squares with two cyclically generated prescribed diagonals, J. Combin. Theory Ser. A 103 (2003) 349-362. (Pubitemid 37052469)
13. M. Grüttmüller, Completing partial Latin squares with prescribed diagonals, Discrete Appl. Math. 138 (2004) 89-97.
14. I.N. Kovalenko, Upper bound on the number of complete mappings, Cybernet. Systems Anal. 32 (1996) 65-68.
15. N.Y. Kuznetsov, Applying fast simulation to find the number of good permutations, Cybernet. Systems Anal. 43 (2007) 830-837. (Pubitemid 350285442)
16. N.Y. Kuznetsov, Estimating the number of good permutations by a modified fast simulation method, Cybernet. Systems Anal. 44 (2008) 547-554.
17. A.A. Levitskaya, A combinatorial problem in the class of permutations over the residue ring Zn modulo odd n, Problemy Upravlen. Inform. (1996) 99-108 (in Russian).
18. B.D. McKay, J.C. McLeod, I.M. Wanless, The number of transversals in a Latin square, Des. Codes Cryptogr. 40 (2006) 269-284. (Pubitemid 44261918)
19. B.D. McKay, I.M. Wanless, On the number of Latin squares, Ann. Comb. 9 (2005) 335-344. (Pubitemid 41407172)
20. H. Niederreiter, K.H. Robinson, Complete mappings of finite fields, J. Aust. Math. Soc. Ser. A 33 (1982) 197-212.
21. W. Nöbauer, Über Permutationspolynome und Permutationsfunktionen für Primzahlpotenzen, Monatsh. Math. 69 (1965) 230-238.
22. W. Nöbauer, Compatible and conservative functions on residue-class rings of the integers, in: Proc. Colloq., Debrecen, 1974, in: Topics in Number Theory, vol. 13, North-Holland, Amsterdam, 1976, pp. 245-257.
23. D. Novakovich, Computation of the number of complete mappings for permutations, Cybernet. Systems Anal. 36 (2000) 244-247.
24. N.J.A. Sloane, The on-line encyclopedia of integer sequences, http://www.research.att.com/~njas/sequences/.
25. D.S. Stones, I.M. Wanless, A congruence connecting Latin rectangles and partial orthomorphisms, submitted for publication.
26. D.S. Stones, I.M. Wanless, Divisors of the number of Latin rectangles, J. Combin. Theory Ser. A 117 (2010) 204-215.
27. G.H.J. van Rees, On Latin queen squares, Congr. Numer. 31 (1981) 267-273.
28. I. Vardi, Computational Recreations in Mathematica, Addison-Wesley, 1991.
29. D.Q. Wan, On a problem of Niederreiter and Robinson about finite fields, J. Aust. Math. Soc. Ser. A 41 (1986) 336-338.
30. I.M. Wanless, Transversals in Latin squares, Quasigroups Related Systems 15 (2007) 169-190.