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/

Zendy Plus

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

Zendy Tools

Zendy Open

Let $\Gamma$ be a group acting on a set $X$. The distinguishing number forthis action of $\Gamma$ on $X$, denoted by $D_{\Gamma}(X)$, is the smallestnatural number $k$ such that the elements of $X$ can be labeled with $k$ labelsso that any label-preserving element of $\Gamma$ fixes all $x \in X$. Inparticular, if the action is faithful, then the only element of $\Gamma$preserving labels is the identity. In this paper, we obtain an upper bound onthe distinguishing number of a set knowing the distinguishing number of a setunder the action of a subgroup. By the concept of motion, we obtain an upperbound for the distinguishing number of a group. Motivated by a problem (Chan2006), we characterize $D_{\Gamma,H}(X)$ which is the smallest number of labelsadmitting a labeling of $X$ such that the only elements of $\Gamma$ that inducelabel-preserving permutations lie in $H$. Finally, we state two algorithms forobtaining an upper and a lower bound for $D_{\Gamma , H}(X)$.

The distinguishing number of groups based on the distinguishing number of subgroups