The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U-duality and whose U-invariant quartic norm ∆(x) determines the lowest order entropy. Here we introduce a Freudenthal duality x→ x̃, for which ̃̃ x = −x. Although distinct from U-duality it nevertheless leaves ∆(x) inva...

We show that for any positive forward density subset N ⊂ Z, there exists N ∈ N , such that, for all n ≥ N , N contains almost perfect n-scaled reproductions of any previously chosen finite set of integers.

We propose an extension to epistemic ATL with perfect recall, past, and distributed knowledge by strategy contexts and demonstrate the strong completeness of a Hilbert-style proof system for its (.U.)-free subset.

Let c(F) be the number of perfect pairs of F and c(G) be the maximum of c(F) over all (near-) one-factorizations F of G. Wagner showed that for odd n, c(Kn) ≥ n∗φ(n) 2 and for m and n which are odd and co-prime to each other, c(Kmn) ≥ 2 ∗ c(Km) ∗ c(Kn). In this note, we establish that both these results are equivalent in the sense that they both give rise to the same lower bound.

V. Chv atal proved that no minimal imperfect graph has a small transversal, that is, a set of vertices of cardinality at most + ! 1 which meets every !-clique and every -stable set. In this paper we prove that a slight generalization of this notion of small transversal leads to a conjecture which is as strong as Berge's Strong Perfect Graph Conjecture for a very large class of graphs, although ...

This paper examines how the fertility of enslaved women was affected by the promise of freedom. Exploiting geographic variation in the effect of the Fugitive Slave Law of 1850, I demonstrate a negative correlation between fertility and the distance to freedom. This negative correlation is stronger on larger plantations but weaker when the slaveholder is a woman. A similar correlation is not pre...

In order to prove the Strong Perfect Graph Conjecture, the existence of a ”simple” property P holding for any minimal non-quasi-parity Berge graph G would really reduce the difficulty of the problem. We prove here that this property cannot be of type ”G is F-free”, where F is any fixed family of Berge graphs.