ENGLISH ABSTRACT: The problem of finding edge-disjoint trees in a hypercube e.g. arises in the context of parallel computing. Independent of applications it is of high aesthetic appeal.

The problem of finding edge-disjoint trees in a hypercube arises for example in the context of parallel computing [3]. Independently of applications it is of high aesthetic appeal. The hypercube of dimension n, denoted ...

The aim of this paper is to provide an affirmative answer to a recent question by Bubeck and Linial on the local profile of trees.

In this paper, we introduce the notion of q-quasiadditivity of arithmetic functions, as well as the related concept of q-quasimultiplicativity, which generalise strong q-additivity and -multiplicativity, respectively. ...

We consider point spectrum traces in the Hofstadter model. We show how to recover the full quantum Hofstadter trace by integrating these point spectrum traces with the appropriate free density of states on the lattice. ...

We investigate the distribution of the number of vertices of a randomly chosen subtree of a tree. Specifically, it is proven that this distribution is close to a Gaussian distribution in an explicitly quantifiable way if ...

For fixed t ≥ 2, we consider the class of representations of 1 as a sum of unit fractions whose denominators are powers of t, or equivalently the class of canonical compact t-ary Huffman codes, or equivalently rooted ...

The quantity that captures the asymptotic value of the maximum number of appearances of a given topological tree (a rooted tree with no vertices of outdegree 1) S with k leaves in an arbitrary tree with sufficiently large ...

A centroid node in a tree is a node for which the sum of the distances to all other nodes attains its minimum, or equivalently a node with the property that none of its branches contains more than half of the other nodes. ...

Given a finite set of bases b1, b2, ..., br (integers greater than 1), a multi-base representation of an integer n is a sum with summands dbα1 1 b α2 2 ··· bαr r , where the αj are nonnegative integers and the digits ...