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Although the character's name sounds native American, he is not. In Double for Death, he explains that his full name is William Tecumseh Sherman Fox, so he was supposedly named for the American Civil War general William Tecumseh Sherman. It seems probable that Stout chose this name in order to justify Fox's nickname, "Tec," which is also a slang term for detective. (A similar motive was presumably behind the naming of another Stout detective, the beautiful Theodolinda "Dol" Bonner.) The surname "Fox" was presumably chosen as an analogy to "Wolf(e)."
Fox's Westchester County is located in the same universe as Wolfe's New York City. Even though the two men seem to be unaware of each other's existence, both are acquainted with operatives from Bonner & Raffray and the Bascom Agency. Characters in both series dine at Rusterman's, dance at the Flamingo Club, frequent the Churchill Hotel, read the Gazette, and drive Wethersill convertibles.
Stout created just three mystery novels with this title character (one of which was adapted into a Wolfe story), before devoting his fiction exclusively to Nero Wolfe stories: