#### Date of Original Version

9-12-2012

#### Type

Article

#### Rights Management

© 2012, Society for Industrial and Applied Mathematics

#### Abstract or Description

Let $B_i^{(k)}$ be the $k$-uniform hypergraph whose vertex set is of the form $S\cup T$, where $|S|=i$, $|T|=k-1$, and $S\cap T=\emptyset$, and whose edges are the $k$-subsets of $S\cup T$ that contain either $S$ or $T$. We derive upper and lower bounds for the Turán density of $B_i^{(k)}$ that are close to each other as $k\to\infty$. We also obtain asymptotically tight bounds for the Turán density of several other infinite families of hypergraphs. The constructions that imply the lower bounds are derived from elementary number theory by probabilistic arguments, and the upper bounds follow from some results of de Caen, Sidorenko, and Keevash.

#### DOI

10.1137/120889009

#### Published In

SIAM Journal on Discrete Mathematics, 26, 4, 1609-1617.