2021/07/28 by Aninda Chakraborty, Chakraborty, Aninda, Sayan Goswami +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2107.13951
openalex publication_date 2021/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we will investigate several new configurations in Ramsey Theory, using the \ostarl,k-operation on the set of integers, recently introduced in \citekey-4. This operation is useful to study symmetric structures in the set of integers, such as monochromatic configurations of the form \ x,y,x+y+xy\ as one of its simplest case. In \citekey-4, the author has studied more general symmetric structures. It has been shown that the Hindman's Theorem, van der Waerden's Theorem, Deuber's Theorem have their own symmetric versions. In this article we will explore several new structures, including polynomial versions of these symmetric structures and some of its variants. As a result, we get several new symmetric polynomial configurations as well as new linear symmetric patterns. In the final section, we will also introduce two new operations on the set of non-negative integers ℕ, to obtain further new configurations.