TITLE: What is this property to be called?
QUESTION [7 upvotes]: Two functions, $f$ and $g$, that satisfy the following identity: $$f(g(a_1,...,a_n), g(b_1,...,b_n),...) = g(f(a_1,b_1,....), f(a_2,b_2,...)...)$$
(notice the "transposition" of the arguments), do they possess a named and/or known property? Or as an alternative, where can I find out more about it?
(Apologies if I asked a duplicate question, but I didn't know how to search for it)

REPLY [2 votes]: In section 5 of
https://www.google.at/url?sa=t&source=web&rct=j&url=https://www.imbs.uci.edu/files/personnel/luce/2000/AczelFalmagneLuce_Mathematica%2520Japonica_2000.pdf&ved=2ahUKEwjS_cWRuqXcAhWNZ1AKHZ7BDGwQFjAEegQIAhAB&usg=AOvVaw3WLjcxovgzVUfeuIABNdBJ
you my find this equation of generalized bisymmetry.