Shuffle identity for iterated integrals
= Shuffle identity for iterated integrals
The product of two coordinate <iterated integrals of a path> is the sum over order-preserving interleavings of their integration variables. Split the product of the two ordered simplices according to the joint order of all variables. This identity explains the algebraic constraints on a geometric <rough path> and the cancellation of low-degree terms in the composition of its local Euler maps.