Mattos, Letícia, Cecchelli, Domenico Mergoni and Parczyk, Olaf (2025) On product Schur triples in the integers. SIAM Journal on Discrete Mathematics, 39 (2). 1082 - 1095. ISSN 0895-4801
Full text not available from this repository.Abstract
Schur’s theorem states that in any k-coloring of the set of integers [n] there is a monochromatic solution to a + b = c , provided n is sufficiently large. Abbott and Wang studied the size of the largest subset of [n] such that there is a k-coloring avoiding a monochromatic a + b = c. This led to the exploration of related problems, such as the minimum number of monochromatic a + b = c in k-colorings of [n] and the probability threshold for a random subset of [n] to have a monochromatic a + b = c in any k-coloring. In this paper, we study natural generalizations of these problems to products ab = c, in deterministic, random, and randomly perturbed environments.
| Item Type: | Article |
|---|---|
| Additional Information: | © 2025 Society for Industrial and Applied Mathematics |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 29 May 2025 13:54 |
| Last Modified: | 29 May 2025 13:54 |
| URI: | http://eprints.lse.ac.uk/id/eprint/128216 |
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