Related papers: Palindromes In Sturmian Strings

Prefix normal words are binary words in which each prefix has at least the same number of $\so$s as any factor of the same length. Firstly introduced by Fici and Lipt\'ak in 2011, the problem of determining the index of the prefix…

We characterize all quasiperiodic Sturmian words: a Sturmian word is not quasiperiodic if and only if it is a Lyndon word. Moreover, we study links between Sturmian morphisms and quasiperiodicity.

Palindromes are strings that read the same forward and backward. The computation of palindromic structures within strings is a fundamental problem in string algorithms, being motivated by potential applications in formal language theory and…

We lift to the multivariate Eulerian polynomials the identity implying that univariate Eulerian polynomials are palindromic. As a consequence of this generalization, we obtain nice combinatorial identities that can be directly extracted…

In a simple pattern matching problem one has a pattern $w$ and a text $t$, which are words over a finite alphabet $\Sigma$. One may ask whether $w$ occurs in $t$, and if so, where? More generally, we may have a set $P$ of patterns and a set…

Palindromes are strings that read the same forward and backward. Problems of computing palindromic structures in strings have been studied for many years with a motivation of their application to biology. The longest palindrome problem is…

Let $D^+$ be the first octant of the Euclidean space and consider the integral cube grid $G$ in $D^+$. The intersections of each line with $G$ form an infinite sequence of three letters which can be considered as an extension of well-known…

The joint spectral radius of a bounded set of $d \times d$ real matrices is defined to be the maximum possible exponential growth rate of products of matrices drawn from that set. For a fixed set of matrices, a sequence of matrices drawn…

We study a class of monic-palindromic polynomials that we call staircase palindromic polynomials. Specifically, suppose $S(x, n, h)$ is a polynomial of degree n with the special form: $S(x; n; h) = x^n + 2x^{n-1} + 3x^{n-2} + \dots + (h -…

Let $G$ be a $p$-group and let $\chi$ be an irreducible character of $G$. The codegree of $\chi$ is given by $|G:\text{ker}(\chi)|/\chi(1)$. If $G$ is a maximal class $p$-group that is normally monomial or has at most three character…

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…

For a compact surface $ S $ with a finite set of marked points $ P $, we define a 1-system to be a collection of arcs which are pairwise non-homotopic and intersect pairwise at most once. We prove that, up to equivalence, there are exactly…

We study two modifications of the Post Correspondence Problem (PCP), namely 1) the bi-infinite version, where it is asked whether there exists a bi-infinite word such that two given morphisms agree on it, and 2) the conjugate version, where…

Given uniform probability on words of length M=Np+k, from an alphabet of size p, consider the probability that a word (i) contains a subsequence of letters (p, p-1,...,1) in that order and (ii) that the maximal length of the disjoint union…

We give an $\mathcal{O}(n \log n)$-time, $\mathcal{O}(n)$-space algorithm for factoring a string into the minimum number of palindromic substrings. That is, given a string $S [1..n]$, in $\mathcal{O}(n \log n)$ time our algorithm returns…

We study the properties of the ternary infinite word p = 012102101021012101021012 ... , that is, the fixed point of the map h:0->01, 1->21, 2->0. We determine its factor complexity, critical exponent, and prove that it is 2-balanced. We…

The palindromic tree (a.k.a. eertree) for a string $S$ of length $n$ is a tree-like data structure that represents the set of all distinct palindromic substrings of $S$, using $O(n)$ space [Rubinchik and Shur, 2018]. It is known that, when…

We define a family of natural decompositions of Sturmian words in Christoffel words, called *reversible Christoffel* (RC) factorizations. They arise from the observation that two Sturmian words with the same language have (almost always)…

We introduce and study natural derivatives for Christoffel and finite standard words, as well as for characteristic Sturmian words. These derivatives, which are realized as inverse images under suitable morphisms, preserve the…

Let $p$ be a prime divisor of the order of a finite group $G$. Then $G$ has at least $2 \sqrt{p-1}$ complex irreducible characters of degrees prime to $p$. In case $p$ is a prime with $\sqrt{p-1}$ an integer this bound is sharp for…