Matthieu Picantin



Petites groupes gaussiens

Thèse de Doctorat de l'Université de Caen (2000)

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Automates, (semi)groupes, dualités

Habilitation à Diriger des Recherches de l'Université Paris Diderot (2017)

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The conjugacy problem in Garside groups

Communications in Algebra 29-3 (2001) 1021–1039

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The center of Garside groups

Journal of Algebra 245-1 (2001) 92–122

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Explicit presentations for the dual braid monoids

C. R. Académie Sciences Paris, Série I 334 (2002) 843–848

ArXiv 0111280

Automatic structures for torus link groups

Journal of Knot Theory & its Ramifications 12-6 (2003) 833–866

ArXiv 0111079

Garside monoids vs divisibility monoids

Mathematical Structures in Computer Science 15-2 (2005) 231–242

ArXiv 0707.0785

Finite transducers for divisibility monoids

Theoretical Computer Science 362 (2006) 207–221

ArXiv 0601328

A new Garside structure for braids groups of type (e,e,r)

with Ruth Corran

Journal of the London Mathematical Society 84-3 (2011) 689–711

ArXiv 0901.0645

On the finiteness problem for automaton (semi)groups

with Ali Akhavi, Ines Klimann, Sylvain Lombardy, and Jean Mairesse

International Journal of Algebra and Computation 22-6 (2012) 1–26

ArXiv 1105.4725

Implementing computations in automaton (semi)groups

with Ines Klimann and Jean Mairesse

17th International Conference on Implementation and Application of Automata (CIAA'12)

Lecture Notes in Computer Science 7381 (2012) 240–252

ArXiv 1310.4856

A characterization of those automata that structurally generate finite groups

with Ines Klimann

11th Latin American symposium on Theoretical INformatics (LATIN'14)

Lecture Notes in Computer Science 8392 (2014) 180–189

ArXiv 1310.7137

Tree products of cyclic groups and HNN extensions

ArXiv 1306.5724


A connected 3-state reversible Mealy automaton cannot generate an infinite Burnside group

with Ines Klimann and Dmytro Savchuk

19th International Conference on Developments in Language Theory (DLT'15)

Lecture Notes in Computer Science 9168 (2015) 313–325

ArXiv 1409.6142

On Torsion-Free Semigroups Generated by Invertible Reversible Mealy Automata

with Thibault Godin and Ines Klimann

9th International Conference on Language and Automata Theory and Applications (LATA'15)

Lecture Notes in Computer Science 8977 (2015) 328–339

ArXiv 1410.4488

Orbit automata as a new tool to attack the order problem in automaton groups

with Ines Klimann and Dmytro Savchuk

Journal of Algebra 445 (2016) 433–457

ArXiv 1411.0158

Automaton (semi)groups: Wang tilings and Schreier tries

with Ines Klimann

Chapter 10 of the book Sequences, Groups, and Number Theory

Trends in Mathematics, ISBN 978-3-319-69152-7

A new hierarchy for automaton semigroups

with Laurent Bartholdi, Thibault Godin, and Ines Klimann

23rd International Conference on Implementation and Application of Automata (CIAA'18)

Lecture Notes in Computer Science 10977 (2018) 71–83

ArXiv 1803.09991

From automatic semigroups to automaton semigroups

46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Leibniz International Proceedings in Informatics 132 (2019) 1–15

ArXiv 1609.09364

Boundary dynamics for bireversible and for contracting automaton groups

with Daniele D'Angeli, Thibault Godin, Ines Klimann, and Emanuele Rodaro

International Journal of Algebra and Computation 30-2 (2020) 431–449

ArXiv 1604.07736

Selfdual lattices and permeable lattices

in preparation

A triple duality in the hyperoctahedral (braid) groups

in preparation

A (not so) wild Garside structure for hyperoctahedral braid groups

in preparation

© Matthieu Picantin