相关论文: Complementary symmetric Rote sequences: the critic…
Complementary symmetric Rote sequences are binary sequences which have factor complexity $\mathcal{C}(n) = 2n$ for all integers $n \geq 1$ and whose languages are closed under the exchange of letters. These sequences are intimately linked…
The asymptotic critical exponent measures for a sequence the maximum repetition rate of factors of growing length. The infimum of asymptotic critical exponents of sequences of a certain class is called the asymptotic repetition threshold of…
We study aperiodic balanced sequences over finite alphabets. A sequence vv of this type is fully characterised by a Sturmian sequence u and two constant gap sequences y and y'. We show that the language of v is eventually dendric and we…
In this paper, we describe minimal string attractors (of size two) of pseudopalindromic prefixes of standard complementary-symmetric Rote sequences. Such a class of Rote sequences forms a subclass of binary generalized pseudostandard…
Using three examples of sequences over a finite alphabet, we want to draw attention to the fact that these sequences having the minimum critical exponent in a given class of sequences show a large degree of symmetry, i.e., they are G-rich…
This study involves definitions for multiple-counting regular and summation sequences of rho. My paper introduces and proves recurrent relationships for multiple-counting sequences and shows their association with Fermat's little theorem. I…
We introduce and study a new complexity function in combinatorics on words, which takes into account the smallest second occurrence time of a factor of an infinite word. We characterize the eventually periodic words and the Sturmian words…
In the asymptotic analysis of regular sequences as defined by Allouche and Shallit, it is usually advisable to study their summatory function because the original sequence has a too fluctuating behaviour. It might be that the process of…
In combinatorics on words, the well-studied factor complexity function $\rho_{\infw{x}}$ of a sequence $\infw{x}$ over a finite alphabet counts, for every nonnegative integer $n$, the number of distinct length-$n$ factors of $\infw{x}$. In…
For a second-order linear differential equation with two irregular singular points of rank three, multiple Laplace-type contour integral solutions are considered. An explicit formula in terms of the Stokes multipliers is derived for the…
We generalize the construction of Roy's Fibonacci type numbers to the case of a Sturmian recurrence and we determine the classical exponents of approximation $\omega_2(\xi)$, $\widehat{\omega}_2(\xi)$, $\lambda_2(\xi)$,…
A collection of complex sequences of length v is complementary if the sum of their periodic autocorrelation function values at all non-zero shifts is constant. For a complex sequence A=[a_0,a_1,...,a_{v-1}] of length v=dm we define the…
The coefficient sequences of multivariate rational functions appear in many areas of combinatorics. Their diagonal coefficient sequences enjoy nice arithmetic and asymptotic properties, and the field of analytic combinatorics in several…
Among all sequences that satisfy a divide-and-conquer recurrence, the sequences that are rational with respect to a numeration system are certainly the most immediate and most essential. Nevertheless, until recently they have not been…
In the last years the attention towards topological dynamical properties of highly discontinuous maps has increased significantly. In [D.Corona, A. Della Corte. The critical exponent functions. Comptes Rendus Math\'ematique, 360(G4),…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
The critical exponent of an infinite word $\bf x$ is the supremum, over all finite nonempty factors $f$, of the exponent of $f$. In this note we show that for all integers $k\geq 2,$ there is a binary infinite $k$-automatic sequence with…
In this paper, given a simple linear recurrence sequence of algebraic numbers, which has either a dominant characteristic root or exactly two characteristic roots of maximal modulus, we give some explicit lower bounds for the index beyond…
The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is…
We prove various results about the largest exponent of a repetition in a factor of the Thue-Morse word, when that factor is considered as a circular word. Our results confirm and generalize previous results of Fitzpatrick and Aberkane &…