4 citations · 21 across the 13 of their papers we have counts for
18 papers
Computing the k-binomial complexity of generalized Thue--Morse words
M. Golafshan, M. Rigo, M. Whiteland
Two finite words are k-binomially equivalent if each subword (i.e., subsequence) of length at most k occurs the same number of times in both words. The k-binomial complexity of an…
Automatic Abelian Complexities of Parikh-Collinear Fixed Points
Michel Rigo, Manon Stipulanti, Markus A. Whiteland
Parikh-collinear morphisms have the property that all the Parikh vectors of the images of letters are collinear, i.e., the associated adjacency matrix has rank 1. In the conference…
q-Parikh Matrices and q-deformed binomial coefficients of words
Antoine Renard, Michel Rigo, Markus A. Whiteland
We have introduced a q-deformation, i.e., a polynomial in q with natural coefficients, of the binomial coefficient of two finite words u and v counting the number of occurrences of…
Introducing q-deformed binomial coefficients of words
Antoine Renard, Michel Rigo, Markus A. Whiteland
Gaussian binomial coefficients are q-analogues of the binomial coefficients of integers. On the other hand, binomial coefficients have been extended to finite words, i.e., elements…
On extended boundary sequences of morphic and Sturmian words
Michel Rigo, Manon Stipulanti, Markus A. Whiteland
Generalizing the notion of the boundary sequence introduced by Chen and Wen, the th term of the -boundary sequence of an infinite word is the finite set of pairs o…
The boundedness and zero isolation problems for weighted automata over nonnegative rationals
Wojciech Czerwiński, Engel Lefaucheux, Filip Mazowiecki +2
We consider linear cost-register automata (equivalent to weighted automata) over the semiring of nonnegative rationals, which generalise probabilistic automata. The two problems of…
Characterizations of families of morphisms and words via binomial complexities
Michel Rigo, Manon Stipulanti, Markus A. Whiteland
Two words are -binomially equivalent if each subword of length at most occurs the same number of times in both words. The -binomial complexity of an infinite word is a co…
The Orbit Problem for Parametric Linear Dynamical Systems
Christel Baier, Florian Funke, Simon Jantsch +7
We study a parametric version of the Kannan-Lipton Orbit Problem for linear dynamical systems. We show decidability in the case of one parameter and Skolem-hardness with two or mor…
On Abelian Closures of Infinite Non-binary Words
Juhani Karhumäki, Svetlana Puzynina, Markus A. Whiteland
Two finite words and are called abelian equivalent if each letter occurs equally many times in both and . The abelian closure of an infinit…
Reachability in Dynamical Systems with Rounding
Christel Baier, Florian Funke, Simon Jantsch +6
We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step. Given a…
Abelian Closures of Infinite Binary Words
Svetlana Puzynina, Markus A. Whiteland
Two finite words and are called Abelian equivalent if each letter occurs equally many times in both and . The abelian closure of (the shift…
Avoiding abelian powers cyclically
Jarkko Peltomäki, Markus A. Whiteland
We study a new notion of cyclic avoidance of abelian powers. A finite word avoids abelian -powers cyclically if for each abelian -power of period occurring in the inf…
On Positivity and Minimality for Second-Order Holonomic Sequences
George Kenison, Oleksiy Klurman, Engel Lefaucheux +5
An infinite sequence of real numbers is holonomic (also known as P-recursive or P-finite) if it satisfies a linear recurrence relation with p…
Every nonnegative real number is an abelian critical exponent
Jarkko Peltomäki, Markus A. Whiteland
The abelian critical exponent of an infinite word is defined as the maximum ratio between the exponent and the period of an abelian power occurring in . It was shown by Fici…
On -abelian Equivalence and Generalized Lagrange Spectra
Jarkko Peltomäki, Markus A. Whiteland
We study the set of -abelian critical exponents of all Sturmian words. It has been proven that in the case this set coincides with the Lagrange spectrum. Thus the sets o…
More on the dynamics of the symbolic square root map
Jarkko Peltomäki, Markus Whiteland
In our earlier paper [A square root map on Sturmian words, Electron. J. Combin. 24.1 (2017)], we introduced a symbolic square root map. Every optimal squareful infinite word co…
On cardinalities of -abelian equivalence classes
Juhani Karhumäki, Svetlana Puzynina, Michaël Rao +1
Two words and are -abelian equivalent if, for each word of length at most , occurs equally many times as a factor in both and . The notion of -abeli…
A square root map on Sturmian words
Jarkko Peltomäki, Markus Whiteland
We introduce a square root map on Sturmian words and study its properties. Given a Sturmian word of slope , there exists exactly six minimal squares in its language (a minimal s…