Purchase Solution

Latin Squares

Not what you're looking for?

Ask Custom Question

1) Show that for n less than or equal to 4, any Latin square of order n can be obtained from the multiplication table of a group by permuting rows, columns, and symbols. Show that this is not true for n=5

2) If n is an order for which mutually orthogonal Latin squares exist, does every Latin square of order n have an orthogonal partner?

Purchase this Solution
Solution Summary

Latin squares are investigated. Multiplication tables of a ground by permuting rows, columns and symbols are determined.

Solution Preview

1) There is a unique group of each order 1, 2, 3, and two of order 4 (up to iso-morphism); check that all these give the Latin squares.
For n = 5, the cyclic group is the only type of group , and gives a Latin square
containing no subsquare of order 2. ...

Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • The origins of Latin

    Latin as the heart of Latin-Romantic language is given particular focus via a set of translations of a particular phrase in varied languages that originated from Latin.

  • Which philosophies have impacted Latin America the most?

    What are some of the philosophies that influenced Latin America? In what way did they impact the cultures of Latin America? ? What contributions to society did folk and elite caudillos bring to Latin American society? ?

  • Latin American Institutions & Colonial Legacy

    329255 Introduction to Latin America Discuss the series of institutions established during the Spanish and Portuguese colonial era in what today is Latin America.

  • Latin Americans - Philosophies, Influence, Contributions

    453497 Latin Americans - Philosophies, Influence, Contributions What are some of the philosophies that influenced Latin America? In what way did they impact the cultures of Latin America?

  • British Economic Involvement in Latin America

    651132 British Economic Involvement in Latin America How did neocolonialism make Latin America after independence resemble regions of Asia and Africa (Chapters 25 & 26) that were subjected to direct colonial rule?

  • Latin American Philosophy

    Policy Toward Latin America, Harvard University Press 1998, Skidmore, Thomas E. and Smith, Peter H., Modern Latin America, Oxford University Press 2005 An influence analysis on Latin American philosophy and its origins.

  • From Latin to Rise of the Vernacular.

    On the Rise of Latin The scholars of Antiquity from the Roman period and towards the Enlightenment used Latin.

  • A Discussion on Latin American Catholicism

    Should Latin American Catholicism be considered polytheistic? Why or why not? How have churches fostered or hindered social changes in Latin America? How has Protestantism spread in Latin America in the past?

  • Colonial Traces: Remaining Hispanic in Latin America

    One can travel across Latin America and be understood when he or she has a good command of Spanish & Portuguese. Latin language then is a principal institution that colonial Latin America retained in their everyday lives. 2.

View More Related Solutions