Let Fq be a finite field with q elements and let X be a set of matrices over Fq. The main results of this paper are explicit expressions for the number of pairs (A,B) of matrices in X such that A has rank r, B has rank s, and A + B has rank k in the cases that (i) X is the set of alternating matrices over Fq and (ii) X is the set of symmetric matrices over Fq for odd q. Our motivation to study ...

It is widely acknowledged that cancers are disorders of cell growth and behavior and that its cause has to be defined at cellular levels. However, studies have shown that the cause of cancer can be deduced from a study of its epidemiology. Sir Percival Pott is credited with linking chemicals to causing cancer when he observed astutely that Chimney sweeps, because of their chronic exposure to so...