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

Let $S$ be a set of $n$ points in general position in the plane, and let$X_{k,\ell}(S)$ be the number of convex $k$-gons with vertices in $S$ that haveexactly $\ell$ points of $S$ in their interior. We prove several equalities forthe numbers $X_{k,\ell}(S)$. This problem is related to the Erd\H{o}s-Szekerestheorem. Some of the obtained equations also extend known equations for thenumbers of empty convex polygons to polygons with interior points. Analogousresults for higher dimension are shown as well.

On weighted sums of numbers of convex polygons in point sets