Sequences of k-reflexivity defects

k-defects as compactons

We argue that topological compactons (solitons with compact support) may be quite common objects if k-fields, i.e., fields with nonstandard kinetic term, are considered, by showing that even for models with well-behaved potentials the unusual kinetic part may lead to a power-like approach to the vacuum, which is a typical signal for the existence of compactons. The related approximate scaling s...

DIMENSIONS OF REFLEXIVITY by

On (n, k)-sequences

An (n; k)-sequence has been studied. A permutation a1; a2; : : : ; akn of 0; 1; : : : ; kn − 1 is an (n; k)-sequence if as+d−as 6≡ at+d−at (mod n) whenever bas+d=nc=bas=nc and bat+d=nc=bat=nc for every s; t and d with 16s¡ t¡ t+d6kn, where bxc is the integer part of x. We recall the “prime construction” of an (n; k)-sequence using a primitive root modulo p whenever kn+1=p is an odd prime. In th...

Constructing k-radius sequences

An n-ary k-radius sequence is a finite sequence of elements taken from an alphabet of size n such that any two distinct elements of the alphabet occur within distance k of each other somewhere in the sequence. These sequences were introduced by Jaromczyk and Lonc to model a caching strategy for computing certain functions on large data sets such as medical images. Let fk(n) be the shortest leng...

Sequences Characterizing k-Trees

A non-decreasing sequence of n integers is the degree sequence of a 1-tree (i.e., an ordinary tree) on n vertices if and only if there are least two 1’s in the sequence, and the sum of the elements is 2(n − 1). We generalize this result in the following ways. First, a natural generalization of this statement is a necessary condition for k-trees, and we show that it is not sufficient for any k >...