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 Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

For an integral convex polytope $\mathcal{P} \subset \mathbb{R}^d$, we recall$L_\mathcal{P}(n)=|n\mathcal{P} \cap \mathbb{Z}^d|$ the Ehrhart polynomial of$\mathcal{P}$. Let $g_r(\mathcal{P})$ be the $r$th coefficients of$L_\mathcal{P}(n)$ for $r=0,\ldots,d$. Martin Henk and Makoto Tagami gave lowerbounds on the coefficients $g_r(\mathcal{P})$ in terms of the volume of$\mathcal{P}$. They proved that these bounds are best possible for $r \in\{1,2,d-2\}$. We show that these bounds are also optimal for $r=3$ and $d-r$even and we give a new best possible bound for $r=d-3$.

Best possible lower bounds on the coefficients of Ehrhart polynomials