A set is called an IP set in a semigroup (S, center dot) if it contains all finite products of a sequence. A set which intersects with all IP sets is known as IP* set. V. Bergelson and N. Hindman proved if A is an IP* set in (N, +), then for any sequence (xn)infinity n=1, there exists a sum subsystem (yn)infinity n=1 such that both FS((yn)infinity n=1) and FP((yn)infinity n=1) are contained in A. S. Goswami asked if we replace the single sequence by l-sequence, then is it possible to obtain a sum subsystem such that all of its zigzag finite sums and products will be in A. He proved that for certain IP* sets (known as dynamical IP* sets) this is possible. In this article, we will show that if A is an IP* set, then for certain l-sequence, there exists a diagonal sum subsystem such that all of its zigzag finite sums and products will be in A. (c) 2023 Elsevier B.V. All rights reserved.
展开▼
