A latin bitrade is a pair of partial latin squares which are disjoint, occupy the same set of non-
empty cells, and whose corresponding rows and columns contain the same sets of symbols …

The concept of a trade in a combinatorial structure has existed for some years now.
However, in the last five years or so there has been a great deal of activity in the area. This …

In this paper, we introduce the concept of the fine triangle intersection problem for a pair of G-
designs, and we consider this problem for kite systems. Let Fin (v)={(s, t):∃ a pair of kite …

The set of integers k for which there exist three latin squares of order n having precisely k
cells identical, with their remaining n 2− k cells different in all three latin squares, denoted by …

In this paper, we give a complete answer to the following question: Given an integer υ≡ 0 or
1 (mod 3) and an integer k, does there exist a twofold triple system of order υ with exactly k …

In this paper the triangle intersection problem for S (2, 4, v) designs is investigated. Let tv= v
(v− 1)/3 and IT (v)={0, 1,…, tv− 30}∪{tv− 27, tv− 24, tv− 18, tv}. Let JT (v)={s| there exist two S …

A latin interchange is a pair of disjoint partial latin squares of the same shape and order
which are row–wise and column–wise mutually balanced. In this paper we document a …

In this paper the triangle intersection problem for a pair of disjoint S (2, 4, v) s is investigated.
Let JT∗(v) denote the set of all integers s such that there exists a pair of disjoint S (2, 4, v) s …

Let Fin (v)={(s, t):∃ a pair of (K4− e)-designs of order v intersecting in s blocks and 2s+ t
triangles}. Let Adm (v)={(s, t): s+ t≤ bv, s∈ J (v), 2s+ t∈ JT (v)}∖{(bv− 3, 1)}, where J (v)(or …

To study orthogonal arrays and signed orthogonal arrays, Ray-Chaudhuri and Singhi (1988
and 1994) considered some module spaces. Here, using a linear algebraic approach we …