Gerechte Designs with Rectangular Regions

A \emph{gerechte framework} is a partition of an $n \times n$ array into $n$ regions of $n$ cells each. A \emph{realization} of a gerechte framework is a latin square of order $n$ with the property that when its cells are partitioned by the framework, each region contains exactly one copy of each symbol. A \emph{gerechte design} is a gerechte framework together with a realization. We investigate gerechte frameworks where each region is a rectangle. It seems plausible that all such frameworks have realizations, and we present some progress towards answering this question. In particular, we show that for all positive integers $s$ and $t$, any gerechte framework where each region is either an $s \times t$ rectangle or a $t\times s$ rectangle is realizable.Comment: 14 pages, 12 figure

Fighting Against Biopiracy: Does the Obligation to Disclose in Patent Applications Truly Help?

In the global fight against biopiracy, one of the key issues is to prevent the grant and exploitation of patents on traditional knowledge and genetic resources by requiring that patent applicants for inventions involving traditional knowledge and genetic resources disclose the source of those resources and provide evidence that the prior informed consent of the local owners of such resources has been obtained and that benefit-sharing agreements have been entered into with those owners. This Article argues that a legal discussion of biopiracy should analyze the obligation to disclose the use of traditional knowledge and genetic resources in an invention beyond the sanctions that are attached in case of violation of such obligations as previously discussed at the international level. These issues should be addressed in light of the key objectives to be achieved: to ensure the effective sharing of benefits resulting from the use of such resources with the local communities that own them, and to implement appropriate mechanisms for this purpose. In the course of the analysis, this Article adopts an interdisciplinary approach by referring to rules governing the legal protection of tangible and intangible cultural property in order to explore the extent to which they could be used as models for a regime of protection against the misappropriation of traditional knowledge and genetic resources. This approach is inspired by the similarity between biopiracy and the misappropriation of cultural property goods, which constitutes a kind of cultural piracy. This Article concludes that balanced, flexible, and interdisciplinary solutions are required in order to ensure that the interests of local communities are protected without unduly threatening the interests of their commercial partners

Variations on the Roy-Gallai theorem

Abstract.: A generalization of the Roy-Gallai Theorem on the chromatic number of a graph is derived which is also an extension of several other results of Berge and of Li. A simple inductive proof is given which provides a direct way of deriving the Theorem of Li. We also show that some classical results valid for optimal colorings cannot be transposed to suboptimal colorings. We finally investigate some elementary properties which are also valid in suboptimal coloring

Weighted stability number of graphs and weighted satisfiability: The two facets of pseudo-Boolean optimization

We exhibit links between pseudo-Boolean optimization, graph theory and logic. We show the equivalence of maximizing a pseudo-Boolean function and finding a maximum weight stable set; symmetrically minimizing a pseudo-Boolean function is shown to be equivalent to solving a weighted satisfiability proble