The interplay between words, computability, algebra and arithmetic has now proved its relevance and fruitfulness. Indeed, the cross-fertilization between formal logic and finite …
Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important …
We introduce efficient data structures for an indexing problem in non-standard stringology— jumbled pattern matching. Moosa and Rahman J. Discr. Alg., 2012 gave an index for …
We derive a simple efficient algorithm for Abelian periods knowing all Abelian squares in a string. An efficient algorithm for the latter problem was given by Cummings and Smyth in …
V Keränen - Theoretical Computer Science, 2009 - Elsevier
In 1961, Paul Erdös posed the question whether abelian squares can be avoided in arbitrarily long words over a finite alphabet. An abelian square is a non-empty word uv …
M Lejeune, M Rigo, M Rosenfeld - Advances in Applied Mathematics, 2020 - Elsevier
Consider k-binomial equivalence: two finite words are equivalent if they share the same subwords of length at most k with the same multiplicities. With this relation, the k-binomial …
We present efficient algorithms computing all Abelian periods of two types in a word. Regular Abelian periods are computed in O (n log log {n}) randomized time which improves …
JD Currie, N Rampersad - Journal of Combinatorial Theory, Series A, 2012 - Elsevier
We show that the problem of whether the fixed point of a morphism avoids Abelian k-powers is decidable under rather general conditions, the most important being that the frequency …
Recently, Constantinescu and Ilie proved a variant of the well-known periodicity theorem of Fine and Wilf in the case of two relatively prime abelian periods and conjectured a result for …