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.

Atmospheric turbulence induced fading is one of the main impairments affecting the operation of free-space optical (FSO) communication systems. In this paper, the bit error rate (BER) of M-ary pulse position modulation (M-ary PPM) of directdetection and avalanche photodiode (APD) based is analyzed. Both log-normal and negative exponential fading channels are evaluated. The investigation discuss...

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

This paper addresses the problem of automatic detection and prediction of abnormal human behaviours in public spaces. For this propose a novel classifier, called N-ary trees, is presented. The classifier processes time series of attributes like the object position, velocity, perimeter and area, to infer the type of action performed. This innovative classifier can detect three types of events: n...

A tree functional is called additive if it satisfies a recursion of the form F (T ) = ∑k j=1 F (Bj)+f(T ), where B1, . . . , Bk are the branches of the tree T and f(T ) is a toll function. We prove a general central limit theorem for additive functionals of d-ary increasing trees under suitable assumptions on the toll function. The same method also applies to generalised planeoriented increasin...

Is it possible to distinguish algebraic from transcendental real numbers by considering the b-ary expansion in some base b 2? In 1950, É. Borel suggested that the answer is no and that for any real irrational algebraic number x and for any base g 2, the g-ary expansion of x should satisfy some of the laws that are shared by almost all numbers. For instance, the frequency where a given finite se...

Is it possible to distinguish algebraic from transcendental real numbers by considering the b-ary expansion in some base b 2? In 1950, É. Borel suggested that the answer is no and that for any real irrational algebraic number x and for any base g 2, the g-ary expansion of x should satisfy some of the laws that are shared by almost all numbers. For instance, the frequency where a given finite se...

fuzzy rough n-ary subhypergroups are introduced and characterized.

In this paper, we give a simple combinatorial explanation of a formula of A. Postnikov relating bicolored rooted trees to bicolored binary trees. We also present generalized formulas for the number of labeled k-ary trees, rooted labeled trees, and labeled plane trees.

We devise a condition strictly between the existence of an $n$-ary and $n{+}1$-ary near-unanimity term. evaluate exactly distributivity modularity levels implied by such condition.