Related papers: Factor Complexity of S-adic sequences generated by…
Any infinite sequence of substitutions with the same matrix of the Pisot type defines a symbolic dynamical system which is minimal. We prove that, to any such sequence, we can associate a compact set (Rauzy fractal) by projection of the…
The $2$-adic complexity has been well-analyzed in the periodic case. However, we are not aware of any theoretical results on the $N$th $2$-adic complexity of any promising candidate for a pseudorandom sequence of finite length $N$ or…
Let $p$ be a prime number and $K$ be a field with embeddings into $\mathbb{R}$ and $\mathbb{Q}_p$. We propose an algorithm that generates continued fraction expansions converging in $\mathbb{Q}_p$ and is expected to simultaneously converge…
Boxicity of a graph $G(V,E)$ is the minimum integer $k$ such that $G$ can be represented as the intersection graph of $k$-dimensional axis parallel rectangles in $\mathbf{R}^k$. Equivalently, it is the minimum number of interval graphs on…
Letting $w$ denote a finite, nonempty word, let $\text{red}(w)$ denote the word obtained from $w$ by replacing every subword $s$ of $w$ of the form $cc \cdots c$ for a given character $c$ (such that there is no character immediately to the…
In this paper, we give a detailed account of the algorithm outlined in [1] for Feynman integral reduction and $\varepsilon$-factorised differential equations. The algorithm consists of two steps. In the first step, we use a new geometric…
An extended formulation of a polyhedron $P$ is a linear description of a polyhedron $Q$ together with a linear map $\pi$ such that $\pi(Q)=P$. These objects are of fundamental importance in polyhedral combinatorics and optimization theory,…
Our goal is to show that both the fast and slow versions of the triangle map (a type of multi-dimensional continued fraction algorithm) in dimension $n$ are ergodic, resolving a conjecture of Messaoudi, Noguiera and Schweiger. This…
Sofic shifts are symbolic dynamical systems defined by the set of bi-infinite sequences on an edge-labeled directed graph, called a presentation. We study the computational complexity of an array of natural decision problems about…
We introduce the factor complex of a neural code, and show how intervals and maximal codewords are captured by the combinatorics of factor complexes. We use these results to obtain algebraic and combinatorial characterizations of…
We study the relation between the palindromic and factor complexity of infinite words. We show that for uniformly recurrent words one has P(n)+P(n+1) \leq \Delta C(n) + 2, for all n \in N. For a large class of words it is a better estimate…
We study some of the factorization invariants of the class of Puiseux monoids generated by geometric sequences, and we compare and contrast them with the known results for numerical monoids generated by arithmetic sequences. The class we…
In the cryptanalysis of stream ciphers and pseudorandom sequences, the notions of linear, jump, and 2-adic complexity arise naturally to measure the (non)randomness of a given string. We define an isometry K on F_q^\infty that is the…
The automaton constrained tree knapsack problem is a variant of the knapsack problem in which the items are associated with the vertices of the tree, and we can select a subset of items that is accepted by a top-down tree automaton. If the…
We provide a complete characterisation of automaticity of uniformly recurrent substitutive sequences in terms of the incidence matrix of the return substitution of the underlying purely substitutive sequence. This resolves a recent question…
We first survey the current state of the art concerning the dynamical properties of multidimensional continued fraction algorithms defined dynamically as piecewise fractional maps and compare them with algorithms based on lattice reduction.…
Pseudo-arclength continuation is a well-established method for generating a numerical curve approximating the solution of an underdetermined system of nonlinear equations. It is an inherently sequential predictor-corrector method in which…
In this paper, we study the complexity of p-adic continued fractions of a rational number, which is the p-adic analogue of the theorem of Lame. We calculate the length of Browkin expansion, and the length of Schneider expansion. Also, some…
We characterize the clustering of a word under the Burrows-Wheeler transform in terms of the resolution of a bounded number of bispecial factors belonging to the language generated by all its powers. We use this criterion to compute, in…
Champarnaud and Ziadi, and Khorsi et al. show how to compute the equation automaton of word regular expression $E$ via the $k$-C-Continuations. Kuske and Meinecke extend the computation of the equation automaton to a regular tree expression…