The aim of this research work is to define and characterize a new class of n-ary multialgebra that may be called canonical (m, n)&minus hypermodules. These are a generalization of canonical n-ary hypergroups, that is a generalization of hypermodules in the sense of canonical and a subclasses of (m, n)&minusary hypermodules. In addition, three isomorphism theorems of module theory and canonical ...

Any complete hypergroup H may be represented as the union g g G H A ∈ =  , where G is a group and the subsets Ag of H satisfy certain properties. With any hypergroupoid 〈H, o〉 we may associate a particular fuzzy set μ . In this paper we determine sufficient and necessary conditions for a finite complete hypergroup 〈H, o〉, where p G (Z , ) ≅ + or 2p G (Z , ) ≅ + , p a prime number, such that t...

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

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.

In this paper we compute the number of reduced decompositions of certain permutations ∈ Sn as a product of transpositions (1; 2), (1; 3), : : :, (1; n). We present several combinatorial correspondences between these decompositions and combinatorial objects such as Catalan paths and k-ary trees. c © 1999 Elsevier Science B.V. All rights reserved