Nonconvexity of the set of hypergraph degree sequences

It is well known that the set of possible degree sequences for a graph on $n$ vertices is the intersection of a lattice and a convex polytope. We show that the set of possible degree sequences for a $k$-uniform hypergraph on $n$ vertices is not the intersection of a lattice and a convex polytope for $k \geq 3$ and $n \geq k+13$. We also show an analogous nonconvexity result for the set of degree sequences of $k$-partite $k$-uniform hypergraphs and the generalized notion of $\lambda$-balanced $k$-uniform hypergraphs.Comment: 5 page

On the commutative quotient of Fomin-Kirillov algebras

The Fomin-Kirillov algebra $\mathcal E_n$ is a noncommutative algebra with a generator for each edge in the complete graph on $n$ vertices. For any graph $G$ on $n$ vertices, let $\mathcal E_G$ be the subalgebra of $\mathcal E_n$ generated by the edges in $G$. We show that the commutative quotient of $\mathcal E_G$ is isomorphic to the Orlik-Terao algebra of $G$. As a consequence, the Hilbert series of this quotient is given by $(-t)^n \chi_G(-t^{-1})$, where $\chi_G$ is the chromatic polynomial of $G$. We also give a reduction algorithm for the graded components of $\mathcal E_G$ that do not vanish in the commutative quotient and show that their structure is described by the combinatorics of noncrossing forests.Comment: 11 pages, 3 figure

Understanding the YouTube generation : how preschoolers process television and YouTube advertising

Preschool children are generally assumed to lack the skills to critically respond to advertising despite being exposed to a high number of advertising messages while watching videos on YouTube. However, research on how preschool children process YouTube advertising is scarce. This study conducts an experiment to examine how preschool children's (4-5 years old, N = 62) responses to video advertising (20-second toy commercial) vary between YouTube and television viewing. The results suggest that almost half of the children were able to distinguish advertising from regular media content, and almost 70% of the children could correctly identify that the video was advertising. No differences were found between the two media. Children were not skeptical toward the video advertisement. With regard to ad effects, the results show low brand and product recall, whereas aided recall was higher (around 40% of the children could correctly recognize the product and brand shown in the advertisement). These findings suggest that 4-5-year-old children already have a proper understanding of advertising, but lack a critical attitude. Furthermore, children's advertising literacy does not vary between YouTube and television advertising