Hexotic Parameters hypothesis works only with Hexotic algorithm. This algorithm is a commercial software.
Name - allows to define the name of the hypothesis (Hexotic Parameters by default).
Nb. Hexes Min Level - allows defining the minimal level of recursive partitioning on the initial octree cube.
Nb. Hexes Max Level - allows defining the maximal level of recursive partitioning on the initial octree cube.
Salome Quadrangles - not documented.
Generate smooth meshes no ridges - specifies that the mesher can ignore ridges. A ridge is a geometrical entity (a sharp edge). The resulting meshes will have better quality elements, at the price of "smoothing" out the geometry.
Authorize invalid elements - specifies that the mesher must conform as much as possible to the geometry (especially the sharp edges). The resulting meshes may contain invalid elements (but with positive volumes: for example, three vertices of an hexahedron on the same edge), for the benefit of better geometry accuracy.