Melodie Andrieu - research

Publications



Journal articles

  1. M. Andrieu, A Rauzy fractal unbounded in all directions of the plane. Comptes Rendus de l'Académie des sciences, 2021. Journal page, Arxiv preprint.
    We construct an Arnoux-Rauzy word whose Rauzy fractal is not contained between two parallel lines. We also give an elementary proof that any Arnoux-Rauzy vector of letters frequencies has rationally independent entries.
  2. M. Andrieu, A. E. Frid, Morphic words and equidistributed sequences. Theoretical Computer Science, 2020 Journal page, ArXiv preprint.
    We discuss numeric sequences arising from the measure of shifts of a pure morphic infinite word, and construct them with morphisms. A software tool for that is provided (demonstration version, download).

    3. Conference articles

  3. M. Andrieu, Autour du déséquilibre des mots C-adiques [text in French], Proceedings of Mons Theoretical Computer Science Days, 2018. Proceedings.
    We contruct C-adic words (= words associated with the Cassaigne-Selmer multidimensional continued fraction algorithm) with infinite imbalance.
  4. M. Andrieu, L. Vivion, Imbalances in hypercubic billiard words. Mons Theoretical Computer Science Days, 2022. Preprint (conference version).
    5. We completely describe the imbalances of words generated by a billiard in a hypercube, for momenta with rationally independent entries.
  5. M. Andrieu, L. Vivion, Minimal complexities for infinite words written with d letters. Invited paper, WORDS, 2023. Proceedings. Preprint.
    6. We discuss the minimal subword complexity and the minimal abelian complexity functions for infinite d-ary words. This leads us to answer a question of Rauzy from 1983: cubic billiard words are a good generalization of Sturmian words for the abelian complexity.

    ...Preprints:

  6. M. Andrieu, Natural coding of minimal rotations of the torus, induction and exduction. Preprint.
    7. This article corrects and deepens the results of Cassaigne, Ferenczi and Zamboni of 2000. We introduce a topological definition of natural coding of a minimal rotation on the d-dimensional torus, inspired by the seminal works of Rauzy on the Tribonacci word. We prove that, under this careful definition, the property of being a natural coding of rotation is preserved by induction and exduction. We apply these results to Arnoux-Rauzy and C-adic words.
  7. M. Andrieu, A semi-algorithm to explore the set of imbalances in a S- adic system. Preprint.
    8. We describe a semi-algorithm consisting of an automaton, or rather, an ever-building family of automata, whose states contain all the possible imbalances of S-adic words, where S is a finite set of substitutions.

    ...Papers to come:

  8. M. Andrieu, L. Vivion, Characterization of imbalances in hypercubic billiard words (journal version).
  9. M. Andrieu, L. Vivion, Abelian complexity of hypercubic billiard words.