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Documents authored by Rosenfeld, Matthieu

Document
DOI: 10.4230/LIPIcs.MFCS.2025.32
A Proof of Shur’s Conjecture on the Growth of Power-Free Languages over Large Alphabets

Authors: Vuong Bui and Matthieu Rosenfeld

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We settle a conjecture of Shur on an estimation of the exponential growth rates of the languages of (n/(n-1))-free words and (n/(n-1)) ^+-free words over large alphabets of size k with a correction of order O (1/(k²)).
Cite as

Vuong Bui and Matthieu Rosenfeld. A Proof of Shur’s Conjecture on the Growth of Power-Free Languages over Large Alphabets. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 32:1-32:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bui_et_al:LIPIcs.MFCS.2025.32,
  author =	{Bui, Vuong and Rosenfeld, Matthieu},
  title =	{{A Proof of Shur’s Conjecture on the Growth of Power-Free Languages over Large Alphabets}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{32:1--32:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.32},
  URN =		{urn:nbn:de:0030-drops-241398},
  doi =		{10.4230/LIPIcs.MFCS.2025.32},
  annote =	{Keywords: power-free languages, large alphabets, Shur’s conjecture, Dejean’s conjecture}
}
Document
DOI: 10.4230/LIPIcs.STACS.2023.52
Reconstructing Words Using Queries on Subwords or Factors

Authors: Gwenaël Richomme and Matthieu Rosenfeld

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
We study word reconstruction problems. Improving a previous result by P. Fleischmann, M. Lejeune, F. Manea, D. Nowotka and M. Rigo, we prove that, for any unknown word w of length n over an alphabet of cardinality k, w can be reconstructed from the number of occurrences as subwords (or scattered factors) of O(k²√{nlog₂(n)}) words. Two previous upper bounds obtained by S. S. Skiena and G. Sundaram are also slightly improved: one when considering information on the existence of subwords instead of on the numbers of their occurrences, and, the other when considering information on the existence of factors.
Cite as

Gwenaël Richomme and Matthieu Rosenfeld. Reconstructing Words Using Queries on Subwords or Factors. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 52:1-52:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{richomme_et_al:LIPIcs.STACS.2023.52,
  author =	{Richomme, Gwena\"{e}l and Rosenfeld, Matthieu},
  title =	{{Reconstructing Words Using Queries on Subwords or Factors}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{52:1--52:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.52},
  URN =		{urn:nbn:de:0030-drops-177041},
  doi =		{10.4230/LIPIcs.STACS.2023.52},
  annote =	{Keywords: Word reconstruction, Subwords, Factors}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2016.81
Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable

Authors: Matthieu Rosenfeld

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
We show that every binary pattern of length greater than 14 is abelian-2-avoidable. The best known upper bound on the length of abelian-2-unavoidable binary pattern was 118, and the best known lower bound is 7. We designed an algorithm to decide, under some reasonable assumptions, if a morphic word avoids a pattern in the abelian sense. This algorithm is then used to show that some binary patterns are abelian-2-avoidable. We finally use this list of abelian-2-avoidable pattern to show our result. We also discuss the avoidability of binary patterns on 3 and 4 letters.
Cite as

Matthieu Rosenfeld. Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 81:1-81:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{rosenfeld:LIPIcs.MFCS.2016.81,
  author =	{Rosenfeld, Matthieu},
  title =	{{Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{81:1--81:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.81},
  URN =		{urn:nbn:de:0030-drops-64892},
  doi =		{10.4230/LIPIcs.MFCS.2016.81},
  annote =	{Keywords: combinatorics on words, pattern avoidance, abelian repetitions}
}
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