Enumeration of Parallelograms in Permutation Matrices for Improved Bounds on the Density of Costas Arrays

The enumeration of Costas arrays of order 28 and its consequences

The results of the enumeration of Costas arrays of order 28 are presented: all arrays found are accounted for by the Golomb and Welch construction methods, making 28 the first order (larger than 5) for which no sporadic Costas arrays exist. The enumeration was performed on several computer clusters and required the equivalent of 70 years of single CPU time. Furthermore, a classification of Cost...

Algebraic Symmetries of Generic Multidimensional Periodic Costas Arrays and their importance in the enumeration of Multidimensional Periodic Sonar Arrays

We present two symmetries of the generic multidimensional periodic Costas arrays over elementary abelian groups. Through exhaustive search, we observe that these two symmetries generate the Costas arrays for the enumeration up to p = 5 (5x5x24). Following the results, we conjecture that these generators characterize the group of symmetries of the generic (m+1)-dimensional periodic Costas arrays...

Lower Bounds of Copson Type for Hausdorff Matrices on Weighted Sequence Spaces

Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply o...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

QUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPS

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...