Patrick Dehornoy
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View article: Some aspects of the SD-world
Some aspects of the SD-world Open
We survey a few of the many results now known about the self-distributivity law and selfdistributive structures, with a special emphasis on the associated word problems and the algorithms solving them in good cases.
View article: Garside combinatorics for Thompson's monoid $F^+$ and a hybrid with the braid monoid $B\_\infty^+$
Garside combinatorics for Thompson's monoid $F^+$ and a hybrid with the braid monoid $B\_\infty^+$ Open
On the model of simple braids, defined to be the left divisors of Garside's elements $Δ\_n$ in the monoid $B\_\infty^+$ , we investigate simple elements in Thompson's monoid $F^+$ and in a larger monoid $H^+$ that is a hybrid of $B\_\infty…
View article: Garside combinatorics for Thompson's monoid $F^+$ and a hybrid with the braid monoid $B_\\infty^+$
Garside combinatorics for Thompson's monoid $F^+$ and a hybrid with the braid monoid $B_\\infty^+$ Open
On the model of simple braids, defined to be the left divisors of Garside's\nelements $\\Delta\\_n$ in the monoid $B\\_\\infty^+$ , we investigate simple\nelements in Thompson's monoid $F^+$ and in a larger monoid $H^+$ that is a\nhybrid o…
View article: A cancellativity criterion for presented monoids
A cancellativity criterion for presented monoids Open
We establish a new, fairly general cancellativity criterion for a presented monoid that properly extends the previously known related criteria. It is based on a new version of the word transformation called factor reversing, and its specif…
View article: A cancellativity criterion for presented monoids
A cancellativity criterion for presented monoids Open
We establish a new, fairly general cancellativity criterion for a presented\nmonoid that properly extends the previously known related criteria. It is based\non a new version of the word transformation called factor reversing, and its\nspe…
View article: The Braid Shelf
The Braid Shelf Open
The braids of $B\_\infty$ can be equipped with a selfdistributive operation $\mathbin{\triangleright}$ enjoying a number of deep properties. This text is a survey of known properties and open questions involving this structure, its quotien…
View article: The Braid Shelf
The Braid Shelf Open
The braids of $B\\_\\infty$ can be equipped with a selfdistributive operation\n$\\mathbin{\\triangleright}$ enjoying a number of deep properties. This text is a\nsurvey of known properties and open questions involving this structure, its\n…
View article: The Braid Shelf
The Braid Shelf Open
The braids of $B_\infty$ can be equipped with a selfdistributive operation $\mathbin{\triangleright}$ enjoying a number of deep properties. This text is a survey of such properties and related open questions.
View article: Frontmatter
Frontmatter Open
GROUPS COMPLEXITY CRYPTOLOGYGROUPS -COMPLEXITY -CRYPTOLOGY is a journal for speedy publication of articles in the areas of combinatorial and computational group theory, complexity theory, and cryptology.Preference is given to papers that t…
View article: Multifraction reduction III: The case of interval monoids
Multifraction reduction III: The case of interval monoids Open
We investigate gcd-monoids, which are cancellative monoids in which any two elements admit a left and a right gcd, and the associated reduction of multifractions (arXiv:1606.08991 and 1606.08995), a general approach to the word problemfor …
View article: Multifraction reduction I: The 3-Ore case and Artin–Tits groups of type FC
Multifraction reduction I: The 3-Ore case and Artin–Tits groups of type FC Open
We describe a new approach to the word problem for Artin–Tits groups and, more generally, for the enveloping group \mathcal U (M) of a monoid M in which any two elements admit a greatest common divisor. The method relies on a rewrite syste…
View article: Multifraction reduction II: Conjectures for Artin-Tits groups
Multifraction reduction II: Conjectures for Artin-Tits groups Open
41 pages ; v2 : cross-references updated ; v3 : exposition improved, typos corrected, final version due tu appear in Journal of Combinatorial Algebra
View article: Multifraction reduction IV: Padding and Artin-Tits groups of sufficiently large type
Multifraction reduction IV: Padding and Artin-Tits groups of sufficiently large type Open
We investigate the padded version of reduction, an extension of multifraction reduction as defined in arXiv:1606.08991, and connect it both with ordinary reduction and with the so-called Property $\mathrm{H}$. As an application, we show th…
View article: Coxeter-like groups for groups of set-theoretic solutions of the Yang–Baxter equation
Coxeter-like groups for groups of set-theoretic solutions of the Yang–Baxter equation Open
We attach witheveryfinite, involutive, nondegenerate set-theoretic solution of the Yang–Baxter equation a finite group that plays for the associated structure group the role that a finite Coxeter group plays for the associated Artin–Tits g…
View article: Multifraction reduction I: The 3-Ore case and Artin-Tits groups of type FC
Multifraction reduction I: The 3-Ore case and Artin-Tits groups of type FC Open
We describe a new approach to the Word Problem for Artin-Tits groups and, more generally, for the enveloping group U(M) of a monoid M in which any two elements admit a greatest common divisor. The method relies on a rewrite system R(M) tha…
View article: Multifraction reduction II: Conjectures for Artin-Tits groups
Multifraction reduction II: Conjectures for Artin-Tits groups Open
Multifraction reduction is a new approach to the word problem for Artin-Tits groups and, more generally, for the enveloping group of a monoid in which any two elements admit a greatest common divisor. This approach is based on a rewrite sy…
View article: Foundations of Garside Theory
Foundations of Garside Theory Open
This text consists of the introduction, table of contents, and bibliography of a long manuscript (703 pages) that is currently submitted for publication. This manuscript develops an extension of Garside's approach to braid groups and provi…
View article: Garside and quadratic normalisation: a survey
Garside and quadratic normalisation: a survey Open
Starting from the seminal example of the greedy normal norm in braid monoids, we analyse the mechanism of the normal form in a Garside monoid and explain how it extends to the more general framework of Garside families. Extending the viewp…
View article: Frontmatter
Frontmatter Open
GROUPS COMPLEXITY CRYPTOLOGYGROUPS -COMPLEXITY -CRYPTOLOGY is a journal for speedy publication of articles in the areas of combinatorial and computational group theory, complexity theory, and cryptology.Preference is given to papers that t…