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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Given a family of $r$-uniform hypergraphs ${\cal F}$ (or $r$-graphs forbrevity), the Tur\'an number $ex(n,{\cal F})$ of ${\cal F}$ is the maximumnumber of edges in an $r$-graph on $n$ vertices that does not contain anymember of ${\cal F}$. A pair $\{u,v\}$ is covered in a hypergraph $G$ if someedge of $G$ contains $\{u,v\}$. Given an $r$-graph $F$ and a positive integer$p\geq n(F)$, let $H^F_p$ denote the $r$-graph obtained as follows. Label thevertices of $F$ as $v_1,\ldots, v_{n(F)}$. Add new vertices $v_{n(F)+1},\ldots,v_p$. For each pair of vertices $v_i,v_j$ not covered in $F$, add a set$B_{i,j}$ of $r-2$ new vertices and the edge $\{v_i,v_j\}\cup B_{i,j}$, wherethe $B_{i,j}$'s are pairwise disjoint over all such pairs $\{i,j\}$. We call$H^F_p$ the expanded $p$-clique with an embedded $F$. For a relatively largefamily of $F$, we show that for all sufficiently large $n$,$ex(n,H^F_p)=|T_r(n,p-1)|$, where $T_r(n,p-1)$ is the balanced complete$(p-1)$-partite $r$-graph on $n$ vertices. We also establish structuralstability of near extremal graphs. Our results generalize or strengthen severalearlier results and provide a class of hypergraphs for which the Tur\'an numberis exactly determined (for large $n$).

Stability and Tur\'an numbers of a class of hypergraphs via Lagrangians