Related papers: Almost Designs and Their Links with Balanced Incom…
We prove three theorems giving extremal bounds on the incidence structures determined by subsets of the points and blocks of a balanced incomplete block design (BIBD). These results generalize and strengthen known bounds on the number of…
Combinatorial $t$-designs have wide applications in coding theory, cryptography, communications and statistics. It is well known that the supports of all codewords with a fixed weight in a code may give a $t$-design. In this paper, we first…
Quasi-logarithmic combinatorial structures are a class of decomposable combinatorial structures which extend the logarithmic class considered by Arratia, Barbour and Tavar\'{e} (2003). In order to obtain asymptotic approximations to their…
Distance-regular graphs are a key concept in Algebraic Combinatorics and have given rise to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we…
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
Balanced incomplete block designs (BIBDs) are a class of designs with v treatments and b blocks of size k that are optimal with regards to a wide range of optimality criteria, but it is not clear which designs to choose for combinations of…
Recall that combinatorial $2s$-designs admit a classical lower bound $b \ge \binom{v}{s}$ on their number of blocks, and that a design meeting this bound is called tight. A long-standing result of Bannai is that there exist only finitely…
This paper is concerned with the characterizations of quasi self-adjoint extensions of a class of formally non-self-adjoint discrete Hamiltonian systems. Some properties of the solutions and the characterization of the minimal linear…
A well known class of objects in combinatorial design theory are {group divisible designs}. Here, we introduce the $q$-analogs of group divisible designs. It turns out that there are interesting connections to scattered subspaces,…
This work presents a recursive construction for simple $t$-designs using resolutions of the ingredient designs. The result extends a construction of $t$-designs in our recent paper [39]. Essentially, the method in [39] describes the blocks…
A nonplanar graph G is called almost-planar if for every edge e of G, at least one of G\e and G/e is planar. In 1990, Gubser characterized 3-connected almost-planar graphs in his dissertation. However, his proof is so long that only a small…
We consider designs for cancer trials which allow each medical centre to treat only a limited number of cancer types with only a limited number of drugs. We specify desirable properties of these designs, and prove some consequences. Then we…
A unitary 2-design can be viewed as a quantum analogue of a 2-universal hash function: it is indistinguishable from a truly random unitary by any procedure that queries it twice. We show that exact unitary 2-designs on n qubits can be…
It has been an open problem whether Hobart's inequality on the parameters of a quasisymmetric 2-design is independent of earlier known restrictions. In this note we show that it is equivalent to inequalities found by Neumaier and…
In this paper, we establish the conditions for some finite abelian groups and the family all the $k$-sets in each of them summing up to an element $x$ to form $t$-designs. We fully characterize the sufficient and necessary conditions for…
We introduce the notion of quasi-orthogonal cocycle. This is motivated in part by the maximal determinant problem for square $\{\pm 1\}$-matrices of size congruent to $2$ modulo $4$. Quasi-orthogonal cocycles are analogous to the orthogonal…
We introduce near triple arrays as binary row-column designs with at most two consecutive values for the replication numbers of symbols, for the intersection sizes of pairs of rows, pairs of columns and pairs of a row and a column. Near…
We try to embed a t-design in a finite commutative group in such a way that the sum of the k points of a block is zero. We can compute the number of blocks of the boolean 2-design having all the non zero vectors of $(Z_2)^n$ as the set of…
We introduce the concept of linked systems of symmetric group divisible designs. The connection with association schemes is established, and as a consequence we obtain an upper bound on the number of symmetric group divisible designs which…
We present a new experimental design procedure that divides a set of experimental units into two groups so that the two groups are balanced on a prespecified set of covariates and being almost as random as complete randomization. Under…