Completeness properties of perturbed sequences

Completeness Properties of Perturbed Sequences

If S is an arbitrary sequence of positive integers, let P(S) be the set of all integers which are representable as a sum of distinct terms of S . Call S complete if P(S) contains all large integers, and subcomplete if P(S) contains an infinite arithmetic progression . It is shown that any sequence can be perturbed in a rather moderate way into a sequence which is not subcomplete . On the other ...

r-COMPLETENESS OF SEQUENCES OF POSITIVE INTEGERS

A complete sequence (an) is a strictly increasing sequence of positive integers such that every su ciently large positive integer is representable as the sum of one or more distinct terms from (an). In this paper, we consider the more general notion of an r-complete sequence where every su ciently large positive integer is now representable as the sum of r or more distinct terms from (an). In p...

NP-completeness of generalized multi-Skolem sequences

A Skolem sequence is a sequence a1, a2, . . . , a2n (where ai ∈ A = {1, . . . , n}), each ai occurs exactly twice in the sequence and the two occurrences are exactly ai positions apart. A set A that can be used to construct Skolem sequences is called a Skolem set. The existence question of deciding which sets of the form A = {1, . . . , n} are Skolem sets was solved by Thoralf Skolem [6] in 195...

Completeness Comparisons a ~ Dng Sequences of Samples

The asymptotic properties of the spectrum of nonsymmetrically perturbed Jacobi matrix sequences

X iv :m at h/ 05 12 22 2v 1 [ m at h. SP ] 1 1 D ec 2 00 5 The asymptotic properties of the spectrum of non symmetrically perturbed Jacobi matrix sequences Leonid Golinskii and Stefano Serra-Capizzano 1 Abstract Under the mild trace-norm assumptions, we show that the eigenvalues of a generic (non Hermitian) complex perturbation of a Jacobi matrix sequence (not necessarily real) are still distri...