Let 
be some object, and 
be operators that can be repeatedly applied on 
. Each sequence 
, gives thus rise to an object that we write as 
(action on the right, most of the time to model an action on positions). We further assume that the operators satisfy the braid relations 
and 
for 
, as well as quadratic relations such as 
. In that case, the image 
can essentially be indexed by the permutation 
, where 
denotes the 
elementary transposition. We denote this image by 
.
The Yang-Baxter graph is the graph whose vertices are labelled by the images 
, and whose edges are labelled by the operators.
In most input and output methods of this domain, permutations are represented by their lexicographically minimal reduced word (see combinat::permutations::reducedWordLexMin); some of the methods do not require the input word to be reduced.
The spectral parameters 
allow to deform the operators. Namely, the image of 
by the 
operator is given by 
.
The value parameter values allows for restricting to an interval of the full permutahedron, in order to take the symmetries of values into account. Namely, 
is only computed if 
is, and the transposition 
makes the word 
strictly smaller (lexicographically?).
