A clique-transversal of a graph G is a subset of vertices that meets all the cliques of G. A clique-independent set is a collection of pairwise vertex-disjoint cliques. A graph G is clique-perfect if the sizes of a minimum clique-transversal and a maximum clique-independent set are equal for every induced subgraph of G. The list of minimal forbidden induced subgraphs for the class of clique-per...

In this paper we study spaces in which each compact subset is a Gδ-set and compare them to H. W. Martin’s c-semi-stratifiable (CSS) spaces, i.e. spaces in which compact sets are Gδ-sets in a uniform way. We prove that a (countably) compact subset of a Hausdorff space X is metrizable and a Gδ-subset of X provided X has a δθ-base, or a point-countable, T1-point-separating open cover, or a quasi-G...

The purpose of this note is to correct a mistake in the article “A curve selection lemma spaces arcs and image Nash map” Compositio Math. 142 (2006), 119–130. It due an overlooked hypothesis definition generically stable subset space X ? variety defined over perfect field k .

Secret sharing is that a dealer distributes a piece of information (called a share) about a secret to each participant such that authorized subsets of participants can reconstruct the secret but unauthorized subsets of participants cannot determine the secret. If any unauthorized subset of participants can not obtain any more information regarding the secret, then the scheme is called perfect. ...

This article examines the geographical corridors for the establishment of rice in seventeenth-century Dutch Guiana. One corridor of introduction is associated with the expulsion of Dutch planters from Brazil in 1644, whose slaves reestablished longstanding subsistence preferences with their exodus to the colony. Another corridor links its introduction to the African Gold Coast, where rice devel...

An (N ;n,m, {w1, . . . , wt})-separating hash family is a set H of N functions h : X −→ Y with |X| = n, |Y | = m, t ≥ 2 having the following property. For any pairwise disjoint subsets C1, . . . , Ct ⊆ X with |Ci| = wi, i = 1, . . . , t, there exists at least one function h ∈ H such that h(C1), h(C2), . . . , h(Ct) are pairwise disjoint. Separating hash families generalize many known combinator...

A secret sharing scheme divides a secret into multiple shares by a dealer and shared among shareholders in such a way that any authorized subset of shareholders can reconstruct the secret; whereas any un-authorized subset of shareholders cannot recover the secret. If the maximal length of shares is equal to the length of the secret in a secret sharing scheme, the scheme is called ideal. If the ...