Given a length m string f over a k-ary alphabet and a positive integer n, we develop eecient algorithms to generate (a) all k-ary strings of length n that have no substring equal to f, (b) all k-ary circular strings of length n that have no substring equal to f, and (c) all k-ary necklaces of length n that have no substring equal to f, where f is an aperiodic necklace. Each of the algorithms ru...

A random m-ary leach tree is constructed from a random permutation of 1, . . . , n. A la of large numbers is obtained for the height Hn of these trees by applying the theory of branching random alks . In particular, it is sho n that Ha/log n y in probability as n ---~ oo, here y = y(m) is a constant depending upon m only. Interestingly, as m ---~ 00 , y(m) is asymptotic to 1/log m, the coeffici...

Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision making problem. The aim of this paper is to apply the concept of fuzzy soft sets to n-ary hypergroup theory. The concepts of (∈(γ), ∈(γ) ∨ q(δ))-fuzzy soft (invertible) n-ary subhypergroups over a commutative n-ary hypergroup are intro...

We investigate the average similarity of random strings as captured by the average number of “cousins” in the underlying tree structures. Analytical techniques including poissonization and the Mellin transform are used for accurate calculation of the mean. The string alphabets we consider are m– ary, and the corresponding trees are m–ary trees. Certain analytic issues arise in the m–ary case th...

In this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (K, ?) are equivalent. For a normal subgroup H of K, we define a weight function ?? on KIH and obtain connection between left amenability of (K, ?) and (K|H, ??). Let H be a compact subhypergroup of K. We define the weight function on K||H and obtain connection...

We determine the dimension of certain q-ary algebraic-geometric codes, extending previous results of Van Der Vlugt for p-ary algebraic-geometric trace codes.

We describe under various conditions abelian subgroups of the automorphism group Aut(Tn) of the regular n-ary tree Tn, which are normalized by the n-ary adding machine τ = (e, . . . , e, τ)στ where στ is the n-cycle (0, 1, . . . , n− 1). As an application, for n = p a prime number, and for n = 4, we prove that every soluble subgroup of Aut(Tn), containing τ is an extension of a torsion-free met...

We consider the problem of broadcasting multiple messages from one processor to many processors in the k-port model for message passing systems. In such systems, processors communicate in rounds, where in every round, each processor can send k messages to k processors and receive k messages from k processors. In this paper, we first present a simple and practical algorithm based on variations o...

Hierarchical classification is supervised multi-class classification problem over the set of class labels organized according to a hierarchy. In this report, we study the work by Ramaswamy et. al. on hierarchical classification over symmetric tree distance loss. We extend the consistency of hierarchical classification algorithm over asymmetric tree distance loss. We design a $\mathcal{O}(nk\log...