A path-hypergraph P (3)(2, 4) is the uniform hypergraph of rank 3, having four vertices and two edges, with exactly two vertices in common. In this paper, the intersection problem among P (3)(2, 4)-designs of order v is studied and completely solved for every admissible v. Mathematics Subject Classification: 05B05

In An asymptotic result on compressed sensing matrices [4], a new construction for compressed sensing matrices using combinatorial design theory was introduced. In this paper, we analyse the performance of these matrices using deterministic and probabilistic methods. We provide a new recovery algorithm and detailed simulations. These simulations suggest that the construction is competitive with...

Let G be a soluble block-transitive automorphism group of 2 − (v, 10, 1) design D. Then G is point-primitive and one of the following holds: (1)if 5 v, then v = pn and G ≤ AΓL(1, pn), where p = 2 is a prime and n a positive integer, and pn ≡ 1(mod90); (2) if 5 | v, then v = 5n, G ≤ AΓL(1, 5n), where n is a positive integer, and pn ≡ 1(mod18) Mathematics Subject Classification: 05B05, 20B25

A projective (2~ n, L, I)-design is a set 9 of n element subsets (called blocks) of a 2nelement set V having the properties that each element of V is a member of 1 blocks and every two blocks have a non-empty intersection. This paper establishes existence and non-existence results for various projective (2n, n, rl, I)-designs and their subdesigns. AMS (MOS) Subject Classifications: Primary 05B0...

A k-bowtie system of order v is a pair (X,B), where X is a finite set of v vertices and B is a collection of edge disjoint k-bowties (called blocks) which partitions the edge set of the complete graph Kn, defined in X. In this paper, for every admissible order v, we construct two disjoint non isomorphic 4-bowtie systems. Mathematics Subject Classification: 05B05

We introduce here two types of balanced nested designs (BND), which are called symmetric and pair-sum BNDs. In this paper, we give a construction for pair-sum BNDs of BIBDs from nested BIBDs and perpendicular arrays. We also give some direct constructions for pair-sum BNDs of BIBDs, based on the result obtained by Wilson (1972). By use of these constructions, we show some constructions for regu...

The energy of a matrix is the sum of its singular values. We study the energy of (0, 1)matrices and present two methods for constructing balanced incomplete block designs whose incidence matrices have the maximum possible energy amongst the family of all (0, 1)-matrices of given order and total number of ones. We also find a new upper bound for the energy of (p, q)-bipartite graphs. AMS Subject...

Let Pk be the path with k vertices and k − 1 edges, k ≥ 4. For every integer v, v ≡ 0 or 1 (mod 2(k − 1)) if k is odd or v ≡ 0 or 1 (mod k−1) if k is even, we produce a Pk-design (V,B) of order v such that no two blocks have k − 1 or k common vertices, i.e. (V,B) is a partial S(k − 1, k, v). AMS classification: 05B05.

The parameters 2 (2λ + 2, λ + 1, λ) are those of a residual Hadamard 2 (4λ + 3, 2λ + 1, λ) design. All 2 (2λ + 2, λ + 1, λ) designs with λ ≤ 4 are embeddable. The existence of non-embeddable Hadamard 2-designs has been determined for the cases λ = 5, λ = 6, and λ = 7. In this paper the existence of an infinite family of non-embeddable 2 (2λ + 2, λ + 1, λ) designs, λ = 3(2m)− 1,m ≥ 1 is establis...

Kuriki and Fuji-Hara (1994) introduced an (r, 2)-design with mutually balanced nested subdesigns ((r, 2)-design with MBN), which is equivalent to a balanced array of strength 2 with s symbols, and gave some constructions of such (r, 2)-designs. In this paper, we consider cyclic orthogonal and balanced arrays, and we give a cyclic version of the results obtained by them. Furthermore, we give a c...