| Abstrakt: |
The paper deals with t-designs that can be partitioned into s-designs, each missing a point of the underlying set, called point-missing s-resolvable t-designs, with emphasis on their applications in constructing t-designs. The problem considered may be viewed as a generalization of overlarge sets which are defined as a partition of all the v + 1 k k-sets chosen from a (v + 1) -set X into (v + 1) mutually disjoint s- (v , k , δ) designs, each missing a different point of X. Among others, it is shown that the existence of a point-missing (t - 1) -resolvable t- (v , k , λ) design leads to the existence of a t- (v , k + 1 , λ ′) design. As a result, we derive various infinite series of 4-designs with constant index using overlarge sets of disjoint Steiner quadruple systems. These have parameters 4- (3 n , 5 , 5) , 4- (3 n + 2 , 5 , 5) and 4- (2 n + 1 , 5 , 5) , for n ≥ 2 , and were unknown until now. We also include a recursive construction of point-missing s-resolvable t-designs and its application. [ABSTRACT FROM AUTHOR] |
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