Journalartikel

Jahr der Veröffentlichung: 1991

Seiten: 25-38

Zeitschrift: Discrete Mathematics

Bandnummer: 97

Heftnummer: 1-3

ISSN: 0012-365X

Open Access Status: Bronze

DOI Link: https://doi.org/10.1016/0012-365X(91)90418-2

Verlag: Elsevier

Abstract: 
We investigate symmetric divisible designs with parameters (m, n, k, lambda-1, lambda-2) with k - lambda-1 = 1. We characterize such designs by their intersection numbers and give a construction method using strongly regular graphs with lambda = mu - 1; we thus obtain a new infinite family of examples. We then consider the special case of symmetric divisible designs with parameters (m, n, k, lambda-1, lambda-2) admitting an abelian Singer group; equivalently, we study abelian divisible difference sets with parameters (m, n, k, k - 1, lambda-2). Improving results of a previous paper, we show that such a DDS is either reversible (i.e., fixed under inversion) and arises from a partial difference set with parameter beta = - 1 (i.e., a strongly regular graph with lambda = mu - 1 admitting a Singer group) or arises (by a new construction) from a Paley Hadamard difference set. In the second case, all possible parameters have been determined. In the first case, the DDS is known to be equivalent to a partial difference set with beta = - 1 (as we have shown in [1]); using this, certain restrictions were obtained in that paper. We will here give two further restrictions, but a complete classification of the possible parameters is as yet missing. However, we can obtain a complete classification of all cyclic divisible difference sets satisfying k - lambda-1 = 1.

Harvard-Zitierstil: ARASU, K., JUNGNICKEL, D. and POTT, A. (1991) SYMMETRICAL DIVISIBLE DESIGNS WITH KAPPA-LAMBDA-1=1, Discrete Mathematics, 97(1-3), pp. 25-38. https://doi.org/10.1016/0012-365X(91)90418-2

APA-Zitierstil: ARASU, K., JUNGNICKEL, D., & POTT, A. (1991). SYMMETRICAL DIVISIBLE DESIGNS WITH KAPPA-LAMBDA-1=1. Discrete Mathematics. 97(1-3), 25-38. https://doi.org/10.1016/0012-365X(91)90418-2