0000000000417308
AUTHOR
ÉLise Prieur-gaston
showing 5 related works from this author
A note on easy and efficient computation of full abelian periods of a word
2016
Constantinescu and Ilie (Bulletin of the EATCS 89, 167-170, 2006) introduced the idea of an Abelian period with head and tail of a finite word. An Abelian period is called full if both the head and the tail are empty. We present a simple and easy-to-implement $O(n\log\log n)$-time algorithm for computing all the full Abelian periods of a word of length $n$ over a constant-size alphabet. Experiments show that our algorithm significantly outperforms the $O(n)$ algorithm proposed by Kociumaka et al. (Proc. of STACS, 245-256, 2013) for the same problem.
Online Computation of Abelian Runs
2015
Given a word $w$ and a Parikh vector $\mathcal{P}$, an abelian run of period $\mathcal{P}$ in $w$ is a maximal occurrence of a substring of $w$ having abelian period $\mathcal{P}$. We give an algorithm that finds all the abelian runs of period $\mathcal{P}$ in a word of length $n$ in time $O(n\times |\mathcal{P}|)$ and space $O(\sigma+|\mathcal{P}|)$.
Abelian Powers and Repetitions in Sturmian Words
2016
Richomme, Saari and Zamboni (J. Lond. Math. Soc. 83: 79-95, 2011) proved that at every position of a Sturmian word starts an abelian power of exponent $k$ for every $k > 0$. We improve on this result by studying the maximum exponents of abelian powers and abelian repetitions (an abelian repetition is an analogue of a fractional power) in Sturmian words. We give a formula for computing the maximum exponent of an abelian power of abelian period $m$ starting at a given position in any Sturmian word of rotation angle $\alpha$. vAs an analogue of the critical exponent, we introduce the abelian critical exponent $A(s_\alpha)$ of a Sturmian word $s_\alpha$ of angle $\alpha$ as the quantity $A(s_\a…
Fast computation of abelian runs
2016
Given a word $w$ and a Parikh vector $\mathcal{P}$, an abelian run of period $\mathcal{P}$ in $w$ is a maximal occurrence of a substring of $w$ having abelian period $\mathcal{P}$. Our main result is an online algorithm that, given a word $w$ of length $n$ over an alphabet of cardinality $\sigma$ and a Parikh vector $\mathcal{P}$, returns all the abelian runs of period $\mathcal{P}$ in $w$ in time $O(n)$ and space $O(\sigma+p)$, where $p$ is the norm of $\mathcal{P}$, i.e., the sum of its components. We also present an online algorithm that computes all the abelian runs with periods of norm $p$ in $w$ in time $O(np)$, for any given norm $p$. Finally, we give an $O(n^2)$-time offline randomi…
Abelian Repetitions in Sturmian Words
2012
We investigate abelian repetitions in Sturmian words. We exploit a bijection between factors of Sturmian words and subintervals of the unitary segment that allows us to study the periods of abelian repetitions by using classical results of elementary Number Theory. We prove that in any Sturmian word the superior limit of the ratio between the maximal exponent of an abelian repetition of period $m$ and $m$ is a number $\geq\sqrt{5}$, and the equality holds for the Fibonacci infinite word. We further prove that the longest prefix of the Fibonacci infinite word that is an abelian repetition of period $F_j$, $j>1$, has length $F_j(F_{j+1}+F_{j-1} +1)-2$ if $j$ is even or $F_j(F_{j+1}+F_{j-1}…