منابع مشابه
Dimensions of Copeland-Erdös Sequences
The base-k Copeland-Erdös sequence given by an infinite set A of positive integers is the infinite sequence CEk(A) formed by concatenating the base-k representations of the elements of A in numerical order. This paper concerns the following four quantities. • The finite-state dimension dimFS(CEk(A)), a finite-state version of classical Hausdorff dimension introduced in 2001. • The finite-state ...
متن کاملBh Sequences in Higher Dimensions
In this article we look at the well-studied upper bounds for |A|, where A ⊂ N is a Bh sequence, and generalise these to the case where A ⊂ N d. In particular we give d-dimensional analogues to results of Chen, Jia, Graham and Green.
متن کاملDucci Sequences in Higher Dimensions
A Ducci sequence is a sequence of n-tuples of integers obtained by iterating the map (a1, . . . , an) !→ (|a1 − a2|, |a2 − a3|, . . . , |an − a1|). In this paper, we generalize the concept of Ducci sequences to sequences of d-dimensional arrays, extend some of the basic results on Ducci sequences to this case, and point out some new phenomena that occur. Our main tool is the description of Ducc...
متن کاملPair Correlations of Sequences in Higher Dimensions
We consider a system of “generalised linear forms” defined on a subset x = (xij) of Rd by
متن کاملThe Dimensions of Individual Strings and Sequences
A constructive version of Hausdorff dimension is developed using constructive supergales, which are betting strategies that generalize the constructive supermartingales used in the theory of individual random sequences. This constructive dimension is used to assign every individual (infinite, binary) sequence S a dimension, which is a real number dim(S) in the interval [0, 1]. Sequences that ar...
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ژورنال
عنوان ژورنال: Information and Computation
سال: 2007
ISSN: 0890-5401
DOI: 10.1016/j.ic.2006.01.006