论文信息 - On strong starters in cyclic groups

On strong starters in cyclic groups

Abstract Strong starters have been very useful in the construction of Room squares and cubes, Howell designs, Kirkman triple systems and Kirkman squares and cubes. In this paper we investigate various properties of strong starters in cyclic groups. In particular, we enumerate all non-isomorphic strong starters in cyclic groups of order n ⩽ 23 and all non-equivalent ones of order n⩽ 27. We also obtain results on the automorphism groups of the corresponding 1-factorizations and their embeddibility in Kirkman triple systems.

[1] W. D. Wallis,et al. The existence of Room squares , 1975 .

[2] Arthur T. White,et al. Permutation Groups and Combinatorial Structures , 1979 .

[3] Douglas R. Stinson,et al. The Spectrum of Room Cubes , 1981, Eur. J. Comb..

[4] P. Lambossy. Sur une manière de différencier les fonctions cycliques d'une forme donnée , 1931 .

[5] R. Mullin,et al. An Existence Theorem for Room Squares* , 1969, Canadian Mathematical Bulletin.

[6] M. Colbourn,et al. On Cyclic Steiner 2-Designs , 1980 .

[7] B. A. Anderson,et al. The Existence of Howell Designs of Even Side , 1984, J. Comb. Theory, Ser. A.

[8] R. Mullin,et al. Construction of Room Squares , 1968 .

[9] Alexander Rosa,et al. On the Existence of Strong Kirkman Cubes of Order 39 and Block Size 3 , 1985 .

[10] S. Bays. Sur les systèmes cycliques de triples de steiner différents pourN premier (ou puissance de nombre premier) de la forme 6n+1 (suite) , 1931 .

[11] Kenneth B. Gross,et al. Some new classes of strong starters , 1975, Discret. Math..

[12] Douglas R. Stinson,et al. A Kirkman square of order 51 and block size 3 , 1985, Discret. Math..

[13] R. Read. Every one a Winner or how to Avoid Isomorphism Search when Cataloguing Combinatorial Configurations , 1978 .