24 citations · 59 across the 11 of their papers we have counts for
12 papers
Mapped Exponent and Asymptotic Critical Exponent of Words
Eva Foster, Aleksi Saarela, Aleksi Vanhatalo
We study how much injective morphisms can increase the repetitiveness of a given word. This question has a few possible variations depending on the meaning of ``repetitiveness''. W…
Mapping words to powers by morphisms
Aleksi Saarela
We characterize the words that can be mapped to arbitrarily high powers by injective morphisms. For all other words, we prove a linear upper bound for the highest power that they c…
A Connection Between Unbordered Partial Words and Sparse Rulers
Aleksi Saarela, Aleksi Vanhatalo
are words that contain, in addition to letters, special symbols called . Two partial words of and $b=b_0 \…
Standard words and solutions of the word equation
Jarkko Peltomäki, Aleksi Saarela
We consider solutions of the word equation such that the squares are minimal squares found in optimal squareful infinite words. We…
Separating many words by counting occurrences of factors
Aleksi Saarela
For a given language , we study the languages such that for all distinct words , there exists a word that appears a different number of times as a fact…
An optimal bound on the solution sets of one-variable word equations and its consequences
Dirk Nowotka, Aleksi Saarela
We solve two long-standing open problems on word equations. Firstly, we prove that a one-variable word equation with constants has either at most three or an infinite number of sol…
Degrees of Infinite Words, Polynomials, and Atoms (Extended Version)
Jörg Endrullis, Juhani Karhumäki Jan Willem Klop, Aleksi Saarela
We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal…
On maximal chains of systems of word equations
Juhani Karhumäki, Aleksi Saarela
We consider systems of word equations and their solution sets. We discuss some fascinating properties of those, namely the size of a maximal independent set of word equations, and…
Systems of word equations, polynomials and linear algebra: A new approach
Aleksi Saarela
We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of…
Variations of the Morse-Hedlund Theorem for -Abelian Equivalence
Juhani Karhumäki, Aleksi Saarela, Luca. Q. Zamboni
In this paper we investigate local to global phenomena for a new family of complexity functions of infinite words indexed by $k \in \Ni \cup \{+\infty\}$ where $\Ni$ denotes the se…
On a generalization of Abelian equivalence and complexity of infinite words
Juhani Karhumaki, Aleksi Saarela, Luca Q. Zamboni
In this paper we introduce and study a family of complexity functions of infinite words indexed by $k \in \ints ^+ \cup {+\infty}.$ Let $k \in \ints ^+ \cup {+\infty}$ and be a…
Systems of Word Equations and Polynomials: a New Approach
Aleksi Saarela
We develop new polynomial methods for studying systems of word equations. We use them to improve some earlier results and to analyze how sizes of systems of word equations satisfyi…