Howell designs with sub-designs

Howell Designs with Sub-designs

A Howell design of side s and order 2n, or more briefly an H(s, 2n), is an s x s array in which each cell is either empty or contains an unordered pair of elements from some (2n)-set V such that (1) every element of V occurs in precisely one cell of each row and each column, and (2) every unordered pair of elements from V is in at most one cell of the array. It follows immediately from the defi...

Sequencings and Howell Designs

On generalized Howell designs with block size three

In this paper, we examine a class of doubly resolvable combinatorial objects. Let t, k, λ, s and v be nonnegative integers, and let X be a set of v symbols. A generalized Howell design, denoted t-GHDk(s, v;λ), is an s × s array, each cell of which is either empty or contains a k-set of symbols from X, called a block, such that: (i) each symbol appears exactly once in each row and in each column...

The Existence of Howell Designs of Even Side

Theta Graph Designs

We solve the design spectrum problem for all theta graphs with 10, 11, 12, 13, 14 and 15 edges.