## 20 Citations

Combinatorial aspects of braids with applications to cryptography

- Mathematics, Computer Science
- 2015

This thesis introduces braids by showcasing a number of equivalent ways of describing what a braid is, and considers algorithms to compute the lcm of a set of braids, which leads to more than one elegant solution to the word problem.

A divisibility result in combinatorics of generalized braids

- MathematicsJ. Comb. Theory, Ser. A
- 2017

Unprovability results involving braids

- Mathematics
- 2011

We construct long sequences of braids that are descending with respect to the standard order of braids (‘Dehornoy order’), and we deduce that, contrary to all usual algebraic properties of braids,…

Computing growth functions of braid monoids and counting vertex-labelled bipartite graphs

- Mathematics, Computer ScienceJ. Comb. Theory, Ser. A
- 2013

Cataland: Why the Fuß?

- Mathematics
- 2019

The three main objects in noncrossing Catalan combinatorics associated to a finite Coxeter system are noncrossing partitions, clusters, and sortable elements. The first two of these have known…

Foundations of Garside Theory

- Mathematics
- 2015

FOUNDATIONS OF GARSIDE THEORYPatrick DEHORNOYwithFranc¸ois DIGNEEddy GODELLEDaan KRAMMERJean MICHELThis text consists of the introduction, table of contents, and bibliography of along manuscript (703…

Still another approach to the braid ordering

- Mathematics
- 2005

We develop a new approach to the linear ordering of the braid group $B_n$, based on investigating its restriction to the set $\Div(\Delta_n^d)$ of all divisors of $\Delta_n^d$ in the monoid…

## References

SHOWING 1-10 OF 40 REFERENCES

ALGORITHMS FOR POSITIVE BRAIDS

- Mathematics
- 1994

We give an easily handled algorithm for the word problem in each of Artin’s braid groups, Bn, based on Garside’s methods, but framed more directly in terms of the set of positive braids in which each…

A new approach to the word and conjugacy problems in the braid groups

- Mathematics
- 1997

Abstract A new presentation of the n -string braid group B n is studied. Using it, a new solution to the word problem in B n is obtained which retains most of the desirable features of the…

Growth Functions and Automatic Groups

- MathematicsExp. Math.
- 1996

It is proved that for a geodesic automatic structure, the growth function for any fixed finite connected graph is a rational function and for a word-hyperbolic group, it is shown that one can choose the denominator of the rational function independently of the finite graph.

Still another approach to the braid ordering

- Mathematics
- 2005

We develop a new approach to the linear ordering of the braid group $B_n$, based on investigating its restriction to the set $\Div(\Delta_n^d)$ of all divisors of $\Delta_n^d$ in the monoid…

New Public-Key Cryptosystem Using Braid Groups

- Computer Science, MathematicsCRYPTO
- 2000

The aim of this article is to show that the braid groups can serve as a good source to enrich cryptography and to propose and implement a new key agreement scheme and public key cryptosystem based on these primitives in thebraid groups.

AN INTRODUCTION TO GARSIDE STRUCTURES

- Mathematics
- 2005

Geometric combinatorialists often study partially ordered sets in which each covering relation has been assigned some sort of label. In this ar- ticle we discuss how each such labeled poset naturally…