Abstract: A Latin square arrangement is an arrangement of s symbols in s rows and s columns, such that every symbol occurs once in each row and each column. When two Latin squares of same order superimposed on one another, then in the resultant array every ordered pair of symbols occurs exactly once, then the two Latin squares are said to be orthogonal. A frequency square M of type F (n; λ) is ...

In this paper we study systems of distinct representatives (SDR’s) and Latin squares, considering SDR’s especially in their application to constructing Latin squares. We give proofs of several important elementary results for SDR’s and Latin squares, in particular Hall’s marriage theorem and lower bounds for the number of Latin squares of each order, and state several other results, such as nec...

A partial latin square on t symbols <rl5..., ut of side n is an n x n matrix, each of the cells of which may be empty or may be occupied by. one of the symbols ol,..., at, and which satisfies the rule that no symbol occurs more than once in any row or more than once in any column. An incomplete latin square on t symbols of side n is a partial latin square in which there are no empty cells; it i...

AIM To investigate the number of publications in cardiovascular disease (CVD) in Latin America and the Caribbean over the last decade. METHODS We performed a bibliometric analysis in PubMed from 2001 to 2010 for Latin America and the Caribbean, the United States, Canada, Europe, China, and India. RESULTS Latin America published 4% of articles compared with 26% from the United States/Canada ...

We introduce orthogonal quantum Latin squares, which restrict to traditional orthogonal Latin squares, and investigate their application in quantum information science. We use quantum Latin squares to build maximally entangled bases, and show how mutually unbiased maximally entangled bases can be constructed in square dimension from orthogonal quantum Latin squares. We also compare our construc...

This paper first reviews some basic properties of cryptographic hash function, secret sharing scheme, and Latin square. Then we discuss why Latin square or its critical set is a good choice for secret representation and its relationship with secret sharing scheme. Further we enumerate the limitations of Latin square in a secret sharing scheme. Finally we propose how to apply cryptographic hash ...

Let n and k be integers, with n > 1 and k > 0. An (n × n)/k semi-Latin square S is an n × n array, whose entries (called blocks) are k-element subsets of a set of size nk, the set of symbols of S, such that each symbol of S occurs exactly once in each row and exactly once in each column of S. Semi-Latin squares form a class of designs generalising Latin squares, and have applications in areas i...

the purpose of this article is to deal with causes and trends of china and latin america foreign policy in hu jintao era. before hu presidency, china had more tendency to promoting relations with the west, but during this period (hu’s era) third world countries like africa and latin america countries gained their precedent positions in china foreign policy. the main question raised here, is “wh...

BACKGROUND This paper focuses on the prevalence of Latin terms and terminological collocations in the issues of Journal of Medical Case Reports (February 2007-August 2017) and discusses the role of Latin terminology in the contemporary process of writing medical case reports. METHODS The objective of the research is to study the frequency of using Latin terminology in English-language medical...