@article {IOPORT.01439495, author = {Nagle, Brendan}, title = {Tur\'an related problems for hypergraphs.}, year = {1999}, journal = {Congressus Numerantium}, volume = {136}, issn = {0384-9864}, pages = {119-127}, publisher = {Utilitas Mathematica Publishing Inc., Winnipeg}, abstract = {Summary: For an $l$-uniform hypergraph ${\cal F}$ and an integer $n$, the Tur\'an number $\text{ex}(n,{\cal F})$ for ${\cal F}$ on $n$ vertices is defined to be the maximum size $|{\cal G}|$ of a hypergraph ${\cal G}\subseteq [n]^l$ not containing a copy of ${\cal F}$ as a subhypergraph. For $l=2$ and ${\cal F}= K^{(2)}_k$, the complete graph on $k$ vertices, these numbers were determined by P. Tur\'an. However, for $l>2$, and nearly any hypergraph ${\cal F}$, the Tur\'an problem of determining the numbers $\text{ex}(n,{\cal F})$ has proved to be very difficult, and very little about these numbers is known. In this survey, we discuss recent results and open problems for triple systems which relate to Tur\'an numbers $\text{ex}(n,{\cal F})$.}, identifier = {01439495}, }