Characterisation of some sparse binary sequential arrays.
Classification of generalized Hadamard matrices and quaternary Hermitian self-dual codes of length 18.
Coalescing Fiedler and core vertices
The nullity of a graph is the multiplicity of zero as an eigenvalue in the spectrum of its adjacency matrix. From the interlacing theorem, derived from Cauchy’s inequalities for matrices, a vertex of a graph can be a core vertex if, on deleting the vertex, the nullity decreases, or a Fiedler vertex, otherwise. We adopt a graph theoretical approach to determine conditions required for the identification of a pair of prescribed types of root vertices of two graphs to form a cut-vertex of unique...
Common Transversals Of Finite Families
Common transversals of finite families.
Complex Hadamard Matrices contained in a Bose–Mesner algebra
Acomplex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying HH* = nI, where * stands for the Hermitian transpose and I is the identity matrix of order n. In this paper, we first determine the image of a certain rational map from the d-dimensional complex projective space to Cd(d+1)/2. Applying this result with d = 3, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose–Mesner algebra of a certain 3-class symmetric...
Computation of rigidity of order for one simple matrix
We shall compute the exact value of rigidity of the triangular matrix with entries 0 and 1.
Connectedness of row and column designs
Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs
Partially supported by the Bulgarian Science Fund contract with TU Varna, No 487.The author developed computer programs needed for the classification of designs with certain automorphisms by the local approach method. All these programs use canonicity test or/and construction of canonical form of an integer matrix. Their efficiency substantially influences the speed of the whole computation. The present paper deals with the implemented canonicity algorithm. It is based on ideas used by McKay, Meringer,...
Control treatments in designs with split units generated by Latin squares
This paper deals with two-factor experiments with split units. The whole plot treatments occur in a repeated Latin square, modified Latin square or Youden square, while subplot treatments occur in a block design within the whole plots. The statistical properties of the considered designs are examined. Special attention is paid to the case where one of the treatments is an individual control or an individual standard treatment. In addition, we give a brief overview of work on the design of experiments...
Correction to the paper "A note on inequivalent Hadamard matrices".
Covering energy of posets and its bounds
The concept of covering energy of a poset is known and its McClelland type bounds are available in the literature. In this paper, we establish formulas for the covering energy of a crown with elements and a fence with elements. A lower bound for the largest eigenvalue of a poset is established. Using this lower bound, we improve the McClelland type bounds for the covering energy for some special classes of posets.
Crooked functions, bent functions, and distance regular graphs.