Smallest weak and smallest totally weak critical sets in the latin squares of order at most seven

A critical set in a latin square of order n is a set of entries in a latin square which can be embedded in precisely one latin square of order n. Also, if any element of the critical set is deleted, the remaining set can be embedded in more than one latin square of order n. In this paper we find smallest weak and smallest totally weak critical sets for all the latin squares of orders six and seven. Moreover, we computationally prove that there is no (totally) weak critical set in the back circulant latin square of order five and we find a totally weak critical set of size seven in the other main class of latin squares of order five.

On the direct product of two weak uniquely completable partial latin squares

In this note we show by counter-example that the direct product of two weak uniquely completable partial latin squares is not necessarily a uniquely completable partial latin square. This counter-example rejects a conjecture by Gower (see [3]) on the direct product of two uniquely completable partial latin squares.

Steiner trades that give rise to completely decomposable latin interchanges

In this paper we focus on the representation of Steiner trades of volume less than or equal to nine and identify those for which the associated partial latin square can be decomposed into six disjoint latin interchanges.

The three-way intersection problem for latin squares

The set of integers k for which there exist three latin squares of order n having precisely k cells identical, with their remaining n(2) - k cells different in all three latin squares, denoted by I-3[n], is determined here for all orders n. In particular, it is shown that I-3[n] = {0,...,n(2) - 15} {n(2) - 12,n(2) - 9,n(2)} for n greater than or equal to 8. (C) 2002 Elsevier Science B.V. All rights reserved.

Latin interchanges and direct products

In this paper we focus on the identification of latin interchanges in latin squares which are the direct product of latin squares of smaller orders. The results we obtain on latin interchanges will be used to identify critical sets in direct products. This work is an extension of research carried out by Stinson and van Rees in 1982.

India, Latin America, and the Caribbean during the Cold War

In this period, the key to the relationship between India and Latin America and the Caribbean (LAC) was based in the political nature of this liaison: it was a "uni-multilateral" relationship, centered in India, where LAC countries operated as a group of autonomous entities (an "island chain" structure), and not as a unit of a supranational character with unified international conduct (an island structure). As we will see, faced with uniform and consistent Indian policies, LAC had national policies which make it impossible to discuss a regional policy towards India. The goal of this work is to form a general characterization of the bilateral policies during the period of the Cold War with the intent of identifying the key explanatory factors of the process. While this may be a limited objective, it addresses the non-existence of an academic debate surrounding the topic. We intend to contribute an analysis which in this phase is primarily descriptive.

Discovering "os ianques do sul": towards an entangled Luso-Hispanic history of Latin America

The article reconstructs the largely forgotten role of key Brazilian intellectuals in the Latins-versus-Anglo-Saxons debates that developed around 1898, emphasizing the embeddedness of their thinking in the transnational crossings of men and ideas within South America. It thus challenges the common depiction of late-nineteenth-century Latin Americanism as a purely Spanish American phenomenon and of the United States as its major catalyst, allowing a more nuanced understanding of this movement' s nature.

Economic sanctions and human rights: an analysis of competing enforcement strategies in Latin America

This article addresses the consequences of economic sanctions for the protection of human rights in Latin America. The literature on sanctions and compliance informs three hypotheses, which investigate the relationship between sanctions and the level of rights protection in two groups of countries: those that were targeted by sanctions and those that were not. Using data from the Political Terror Scale (PTS) and from Freedom House, I find empirical evidence that sanctions do improve the level of protection in countries that were not targeted. This finding can be explained by the deterrent effect attributed to sanctions by the compliance literature, broadly interpreted. The presence of economic sanctions in a given year increases the probability of observing better human rights practices by almost 50%. These results hold for the 12 Latin American countries that were not subject to economic sanctions for the period 1976-2004.