2 citations · 3 across the 7 of their papers we have counts for
11 papers
Free augmented LD-systems
Patrick Dehornoy
Define an augmented LD-system, or ALD-system, to be a set equipped with two binary operations, one satisfying the left self-distributivity law and…
Still another approach to the braid ordering
Patrick Dehornoy
We develop a new approach to the linear ordering of the braid group , based on investigating its restriction to the set $\Div(Δ\_n^d)$ of all divisors of in the mono…
On word reversing in braid groups
Patrick Dehornoy, Bert Wiest
It has been conjectured that in a braid group, or more generally in a Garside group, applying any sequence of monotone equivalences and word reversings can increase the length of a…
The group of parenthesized braids
Patrick Dehornoy
We investigate a group that includes Artin's braid group and Thompson's group . The elements of are represented by braids diagrams in which…
Geometric presentations for Thompson's groups
Patrick Dehornoy
We prove that Thompson's groups and are the geometry groups of associativity, and of associativity together with commutativity, respectively. We deduce new presentations of…
Braids in trivial braid diagrams
Patrick Dehornoy
We show that every trivial 3-strand braid diagram contains a disk, defined as a ribbon ending in opposed crossings. Under a convenient algebraic form, the result extends to every A…