3-complementary frames and doubly near resolvable (v,3,2)- BIBDs

Existence of doubly near resolvable (v, 4, 3) BIBDs

The existence of doubly near resolvable (v, 2, 1)-BIBDs was established by Mullin and Wallis in 1975. For doubly near resolvable (v, 3, 2)-BIBDs, the existence problem was investigated by Lamken in 1994, and completed by Abel, Lamken and Wang in 2007. In this paper, we look at doubly near resolvable (v, 4, 3)-BIBDs; we establish that these exist whenever v ≡ 1 (mod 4) except for v = 9 and possi...

Some new near resolvable BIBDs with k=7 and resolvable BIBDs with k=5

The Existence of Kirkman Squares-Doubly Resolvable (v, 3, 1)-BIBDs

A Kirkman square with index λ, latinicity μ, block size k, and v points, KSk(v; μ, λ), is a t × t array (t = λ(v − 1)/μ(k − 1)) defined on a v-set V such that (1) every point of V is contained in precisely μ cells of each row and column, (2) each cell of the array is either empty or contains a k-subset of V , and (3) the collection of blocks obtained from the non-empty cells of the array is a (...

Doubly near resolvable m-cycle systems

An m-cycle system C of λKn is said to be near resolvable if the mcycles in C can be partitioned into near parallel classes R1, R2, . . . , Rλn/2, each one of which is a 2-factor of λKn − v for some vertex v in λKn. If an NR(n,m, λ)-CS has a pair of orthogonal resolutions, it is said to be doubly resolvable and is denoted by DNR(n,m, λ)-CS. For m = 2, 3, DNR(n,m, 2)-CSs are known as Room frames ...

Existence of near resolvable (v, k, k-1) BIBDs with k∈{9, 12, 16}

A necessary condition for existence of a (v, k, k−1) near resolvable BIBD is v ≡ 1 (mod k). In this paper, we update earlier known existence results when k ∈ {9, 12, 16}, and show this necessary condition is sufficient, except possibly for 26, 37 and 149 values of v for k = 9, 12, 16 respectively. Some new results for existence of (9, 8)-frames of type 9 are also obtained; in particular, we sho...