Finally, in the paper we show two algebras over the operad of posets, and each algebra is split into three isomorphic algebras.

We conjecture that this is a general result, certain algebras over the operad of posets come in triples. We are working on the formalization of this statement, but we have evidence.
I probably have to clarify that we proved that series parallel posets preserve the enumeration of shuffles, but I suposse this is true for arbitrary posets. And we believe to prove the general result we may need a version of Ehrhart theory. #Shuffles #OperadicCombinatorics 3/3