arXiv:2402.09053 Abstract | arXiv Analytics

arXiv:2402.09053 [math.CO]Abstract References Reviews Resources

Cartesian products of two $CR$ sets

Published 2024-02-14, updated 2024-06-16Version 2

The notions of CR set is intimately related with the generalized van der Waerden's theorem. In this article, we prove the product of two CR sets is again a CR set. This answers [Question 4.2., N. Hindman, H. Hosseini, D. Strauss, and M. Tootkaboni: Combinatorially rich sets in arbitrary semigroups, Semigroup Forum, 107 (2023), 127-143.] . We use combinatorial arguments to prove our result.

Comments: Semigroup Forum: to appear

Categories: math.CO

Subjects: 05D10, 22A15, 54D35

Keywords: cartesian products, cr set, generalized van der waerdens theorem, combinatorial arguments, combinatorially rich sets

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