Perfect Maps are two-dimensional arrays in which every possible sub-array of a certain size occurs exactly once. They are a generalisation of the de Bruijn sequences to two dimensions and are of practical significance in certain position location applications. In such applications the decoding problem, i.e. resolving the position of a particular sub-array within a specified Perfect Map, is of g...

The vertex boundary-width problem (for short VBWP) is to determine the value of vbw(G)=max1 |V |minS⊆V,|S|= |N(S)| for a given graph G= (V ,E), where N(S)= {v / ∈ S|v is a neighbor of u for some u ∈ S}. In this paper, we give a lower bound for vertex boundary-width of complete k-ary trees. © 2007 Elsevier B.V. All rights reserved.

Following [1], in this note we compute the average number of protected points in all k-ary trees with n internal points.

we describe under various conditions abelian subgroups of the automorphism‎ ‎group $mathrm{aut}(t_{n})$ of the regular $n$-ary tree $t_{n}$‎, ‎which are‎ ‎normalized by the $n$-ary adding machine $tau =(e‎, ‎dots‎, ‎e,tau )sigma _{tau‎ ‎}$ where $sigma _{tau }$ is the $n$-cycle $left( 0,1‎, ‎dots‎, ‎n-1right) $‎. ‎as‎ ‎an application‎, ‎for $n=p$ a prime number‎, ‎and for $n=4$‎, ‎we prove that...

In this paper, we propose a novel transmission scheme, called sparse layered MIMO (SL-MIMO), that combines non-orthogonal and singular value decomposition (SVD) precoding. Non-orthogonality in SL-MIMO allows re-using of the eigen-channels which improves spectral efficiency error rate performanc...

In this paper, we determine the expectation and variance of Xn the external path length in a random recursive k-ary tree of size n.

We provide strong theoretical and experimental evidence that standard sub-tree crossover with uniform selection of crossover points pushes a population of a-ary GP trees towards a distribution of tree sizes of the form: Pr{n} = (1− apa) ( an+ 1 n ) (1− pa) pa where n is the number of internal nodes in a tree and pa is a constant. This result generalises the result previously reported for the ca...

Computing with sets of tuples (n-ary relations) is often required in programming. This paper presents a new data structure dedicated to the manipulation of large sets of tuples, dubbed sharing tree. The main idea is to share in memory some sub-tuples of the set. We give algorithms for common set operations, that have theoretical complexities proportional to the sizes of the sharing trees given ...

We prove that any IN-rational sequence s = (sn) n1 of non-negative integers satisfying the Kraft strict inequality P n1 snk ?n < 1 is the enumerative sequence of leaves by height of a rational k-ary tree. Particular cases of this result had been previously proven. We give some partial results in the equality case.