Characterizing follower and extender set sequences

Global square sequences in extender models

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 >...

Set Sequences and Monotone Class

In this paper we first defined the partial-union sequence, the partial-intersection sequence, and the partial-difference-union sequence of given sequence of subsets, and then proved the additive theorem of infinite sequences and sub-additive theorem of finite sequences for probability. Further, we defined the monotone class of families of subsets, and discussed the relations between the monoton...

Characterizing leader sequences of CRISPR loci

MOTIVATION The CRISPR-Cas system is an adaptive immune system in many archaea and bacteria, which provides resistance against invading genetic elements. The first phase of CRISPR-Cas immunity is called adaptation, in which small DNA fragments are excised from genetic elements and are inserted into a CRISPR array generally adjacent to its so called leader sequence at one end of the array. It has...

Sequences of characters characterizing countable groups

We show, that for every countable subgroup H of a compact abelian metrizable group G there exists a characterizing sequence of characters (χn)n, i.e. α ∈ H iff ‖χn(α)‖ → 0. The introduced methods allow to answer questions stated in [2] and [9]. Acknowledgements: The authors are very grateful to András Biró and Vera T. Sós for their substantial contributions to this article. Moreover they thank ...