An extension theorem for t-designs |
| |
Authors: | Michel Sebille |
| |
Affiliation: | Département de Mathématiques, Campus Plaine C.P. 216, Université Libre de Bruxelles, Boulevard du Triomphe B - 1050 Bruxelles, Belgium |
| |
Abstract: | In 1994, van Trung (Discrete Math. 128 (1994) 337–348) [9] proved that if, for some positive integers d and h, there exists an Sλ(t,k,v) such thatthen there exists an Sλ(v−t+1)(t,k,v+1) having v+1 pairwise disjoint subdesigns Sλ(t,k,v). Moreover, if Bi and Bj are any two blocks belonging to two distinct such subdesigns, then d|Bi∩Bj|<k−h. In 1999, Baudelet and Sebille (J. Combin. Des. 7 (1999) 107–112) proved that if, for some positive integers, there exists an Sλ(t,k,v) such thatwhere m=min{s,v−k} and n=min{i,t}, then there exists anhaving pairwise disjoint subdesigns Sλ(t,k,v). The purpose of this paper is to generalize these two constructions in order to produce a new recursive construction of t-designs and a new extension theorem of t-designs. |
| |
Keywords: | t-design Recursive construction Extension of designs |
本文献已被 ScienceDirect 等数据库收录! |
|