I am interested in the following class of knots $K$:


$\{$$K$ has a braid presentation such that for any fixed position $k$, either only positive or negative powers of $\sigma\_k$ appear in the braid word$\}$ (For example, $\sigma\_1 \sigma\_2^{-1}\sigma\_1 \sigma\_2^{-1}$ would be an instance of such a braid.)


My first question is: Is there a name for this class of knots? If so, I would greatly appreciate any suggestion of reference on this class of knots.


It seems like, at least for knots with small number of crossings, they are fibered. So my second question is whether it is true in general that any such knot is fibered.



Knots with a braid presentation with only positive or negative crossings on each fixed position
The braids that you're talking about are called *homogeneous* braids. I don't know that closures of homogeneous braids have a name, though. (There is something called "homogeneous knot", but the class of homogeneous knots strictly contains the set of closures of homogeneous braids.)


Stallings [proved](https://www.maths.ed.ac.uk/%7Ev1ranick/papers/stallfib2.pdf) that the closure of a homogeneous braid is fibred.


