Given a sequence (Xn) of random variables, Xn is said to be near-record if Xn∈(Mn−1−a,Mn−1], where Mn=max{X1, …, Xn} and a>0 parameter. We investigate the point process η on [0,∞) values from an integer-valued, independent identically distributed sequence, showing that it Bernoulli cluster process. derive probability generating functional formulas for expectation, variance covariance countin...

We study a process of generating random positive integer weight sequences $$\{ W_n \}$$ where the gaps between weights X_n = - W_{n-1} are i.i.d. integer-valued variables. The main result paper is that if gap distribution has moment function with large enough radius convergence, then sequence almost surely asymptotically m-complete for every $$m\ge 2$$ , i.e. multiple greatest common divisor (g...

A non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized Fibonacci sequence , , , . A remarkable application of this definition may be find on the study of random covers in the cryptography. The 2-step generalized sequences for the dihedral groups studi...

We define Bn to be the set of n-tuples of the form (a0, . . . , an−1) where aj = ±1. If A ∈ Bn, then we call A a binary sequence and define the autocorrelations of A by ck := ∑n−k−1 j=0 ajaj+k for 0 k n− 1. The problem of finding binary sequences with autocorrelations ‘near zero’ has arisen in communications engineering and is also relevant to conjectures of Littlewood and Erdős on ‘flat’ polyn...