A Turk's head link 
is the closure of the braid 
on 
strands, for positive integers 
and 
. For 
, the braid is trivial. Here 
are the standard generators of the braid
group. The link has 
components, where 
denotes the greatest common divisor. When
this number is one, it is a Turk's head knot (Di
Prisa and Savk 2026).
For the orientation in which all strands run in the same direction, Stanggassinger (2026) proved Takemura's conjectured relation between the Conway
polynomials of 
and 
.
If their respective coefficients of 
are 
and 
, then 
for 
and 
for 
. Takemura (2016) had proved the cases 
and 
. Stanggassinger (2026) credits Claude Code with developing
the proof and algorithms under his direction.
and 
: A Proof of Takemura's Conjecture." 23 Oct 2026.
- and 
-Turk's Head Links." J. Knot Theory Ramifications 25,
1650082, 2016.