One is known as the 'Dan Dare' or 'Mickey Mouse' cap which is a skull cap with a narrow rim around the top for bachelors; the other was known as the tricorn or upside-down iron, which was basically a mortarboard but with a triangle instead of a square for the top board for masters.
She has also mentioned several other influences specific to the "Tejada" series, such as Delano Ames' The Man in the Tricorn Hat, and Carmen Martín Gaite's El cuarto de atrás (aka The Back Room).