Representations of $(2,n)$-semigroups by multiplace functions
  We describe the representations of $(2,n)$-semigroups, i.e. groupoids with $n$ binary associative operations, by partial $n$-place functions and prove that any such representation is a union of some family of representations induced by Schein's determining pairs. 
Wieslaw A. Dudek, Valentin S. Trokhimenko