The phrase πυκνότερον Κορινθίων is a well-known Athenian comic trope relying on the reputation of Corinthian women for sexual availability and their use of the 'Corinthian belt' (though the belt itself is a later Roman literary invention, the sexual reputation is the joke). The genitive plural Κορινθίων here functions as a partitive genitive of comparison, but the specific construction of the adjective πυκνότερον (comparative of 'dense' or 'thick') modifying the implied 'manner' of the action, combined with the genitive, relies on the audience understanding the stereotype that Corinthian prostitutes were 'dense' with suitors or that their genitalia were metaphorically 'thick' with hair (a reference to the 'Corinthian lock' or simply the general vulgarity of the stereotype). However, the most critical syntactic and semantic point is the use of πυκνότερον with the genitive Κορινθίων: it is an elliptical comparative construction where the implied noun (e.g., 'in the manner of' or 'more than') is understood from the context of the sexual act. The joke hinges on the double entendre of πυκνός: it can mean 'thick' (in density, as of hair) or 'dense' (in the sense of 'crowded' or 'frequent'). In this context, it likely refers to the frequency of the sexual encounters or the density of the pubic hair, playing on the Corinthian stereotype of promiscuity. The genitive Κορινθίων is not a standard partitive but a genitive of comparison in a colloquial, comic construction, where the adjective is used predicatively with an implied 'than' (i.e., 'you drag it more densely than the Corinthians [do]').