A latin bitrade (T , T⊗) is a pair of partial latin squares which are disjoint, occupy the same set of non-empty cells, and whose corresponding rows and columns contain the same set of entries. A genus may be associated to a latin bitrade by constructing an embedding of the underlying graph in an oriented surface. We report computational enumeration results on the number of spherical (genus 0) ...

We show how to produce algebraically a complete orthogonal set of Latin squares from a left quasifield and how to generate algebraically a maximal set of self-orthogonal Latin squares from a left nearfield. For a left Veblen-Wedderburn system, we establish the algebraic relationships between the standard projective plane construction of a complete set of Latin squares, our projective plane cons...

In this paper, we combine the notions of completing and avoiding partial latin squares. Let P be a partial latin square of order n and let Q be the set of partial latin squares of order n that avoid P . We say that P is Q -completable if P can be completed to a latin square that avoids Q ∈ Q. We prove that if P has order 4t and contains at most t − 1 entries, then P is Q -completable for each Q...

In this paper we consider the problem of enumerating diagonal Latin squares of small order. In particular we discuss possible algorithmic approaches to this problem and show our results in this regard. Surprisingly, our research showed that the best algorithm for enumerating diagonal Latin squares consists of a number of fixed loops, and its effectiveness can be significantly increased by caref...

Author: Jenny Zhang First, let’s preview what mutually orthogonal Latin squares are. Two Latin squares L1 = [aij ] and L2 = [bij ] on symbols {1, 2, ...n}, are said to be orthogonal if every ordered pair of symbols occurs exactly once among the n2 pairs (aij , bij), 1 ≤ i ≤ n, 1 ≤ j ≤ n. Now, let me introduce a related concept which is called transversal. A transversal of a Latin square is a se...

The Latin hypercube design is a popular choice of experimental design when computer simulation is used to study a physical process. These designs guarantee uniform samples for the marginal distribution of each single input. A number of methods have been proposed for extending the uniform sampling to higher dimensions. We show how to construct Latin hypercube designs in which all main effects ar...

We undertake an investigation of combinatorial designs engendered by cellular automata (CA), focusing in particular on orthogonal Latin squares and orthogonal arrays. The motivation is of cryptographic nature. Indeed, we consider the problem of employing CA to define threshold secret sharing schemes via orthogonal Latin squares. We first show how to generate Latin squares through bipermutive CA...

hav We are proud to present this special issue of Value in Health: Pharmacoeconomics and Outcomes Research in Latin America. We resent a combination of plenary summaries presented at the nternational Society of Pharmacoeconomics and Outcomes Reearch (ISPOR) Second Latin America Conference held in Brazil uring September 2009, and original research studies conucted in our region. We think this co...

The average Latin American country produces about 1 fifth of the output per worker of the US. What are the sources of these enormous income gaps? I report development-accounting results for Latin America. On average Latin America’s overall physical and human capital endowment relative to the USA is essentially identical to Latin America’s efficiency relative to the USA . In my main sample avera...

Although lexicography of Latin has a long tradition dating back to ancient grammarians, and almost all Latin grammars devote to wordformation at least one part of the section(s) concerning morphology, none of the today available lexical resources and NLP tools of Latin feature a wordformation-based organization of the Latin lexicon. In this paper, we describe the first steps towards the semi-au...