Cartesian product of some combinatorially rich sets

2019/12/19 by Sayan Goswami, Goswami, Sayan
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1912.09965

13 pages

arxiv created 2019/12/19 · arxiv updated 2019/12/23

Abstract

N. Hindman and D. Strauss had shown that, for discrete semigroups, the cartesian product of two central sets are central. They also proved that the product of J- sets and C-sets are also J-set and C-set and characterized when the infnite product of these sets are preserved. To prove these results they used the algebraic structure of Stone-Cech compactification of discrete semigroups. In this work we will give a combinatorial proof of the preserveness of those large sets under fnite cartesian product.

Related

• Cartesian product of combinatorially rich sets -- algebraic, elementary and dynamical approaches
• Cartesian products of two CR sets
• A combinatorial approach to central to theorem
• Essential CR set near zero
• Central Sets Theorem along filters and some combinatorial consequences