An answer to Goswami's question and new sources of IP^-sets containing combined zigzag structure

A set is called $IP$-set in a semigroup (S,· ) if it contains finite products of a sequence. A set that intersects with all $IP$-sets is called IP^-set. It is a well known and established result by Bergelson and Hindman that if A is an IP^-set, then for any sequence xₙₙ₌₁∞, there exists a sum subsystem yₙₙ₌₁∞ such that FS( yₙₙ₌₁∞)∪ FP( yₙₙ₌₁∞)⊂ A. In [Question 3]{G}, S. Goswami posed the question: if we replace the single sequence by l-sequences, then is it possible to obtain a sum subsystem such that all of its zigzag finite sums and products will be in A. Goswami has given affirmative answers only for dynamical IP^-sets which are not equivalent to those of IP^-sets, but are rather significantly stronger. In this article, we will give the answer to Goswami's question that was unknown until now.