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...

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.