English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

For a given positive integer $k$, the Sidon-Ramsey number $\SR(k)$ is definedas the minimum value of $n$ such that, in every partition of the set $[1, n]$into $k$ parts, there exists a part that contains two distinct pairs of numberswith the same sum. In other words, there is a part that is not a Sidon set. Inthis paper, we investigate the asymptotic behavior of this parameter and twogeneralizations of it. The first generalization involves replacing pairs ofnumbers with $h$-tuples, such that in every partition of $[1, n]$ into $k$parts, there exists a part that contains two distinct $h$-tuples with the samesum. Alternatively, there is a part that is not a $B_h$ set. The secondgeneralization considers the scenario where the interval $[1, n]$ issubstituted with a non-necessarily symmetric $d$-dimensional box of the form$\prod_{i=1}^d[1,n_i]$. For the general case of $h\geq 3$ and non-symmetricboxes, before applying our method to obtain the Ramsey-type result, we neededto establish an upper bound for the corresponding density parameter.

Sidon-Ramsey and $B_{h}$-Ramsey numbers