Difference sets: extraneous multipliers and Abelianization /
Xiaohong Wu · OhioLink ETD Center (Ohio Library and Information Network) · 1994
C h ap ter I In trod u ctionIn this chapter, we will introduce some background of difference sets, one of the most fascinating subjects in the design theory of combinatorics.In order to understand both the elegance and complexity of difference sets, we have to start with basics of design theory.We assume basic knowledge of group theory and group ring theory.Al most any graduate text book on algebra will suffice as a reference book for group theory assumed here.As for group ring theory, we recommend Ho B .M a n n 's book.Combinatorial design problems originated from ancient recreational prob lems.They become an im portant field in mathematics because of their ap plications in statistics and even in engineering, like in coding.One of the most famous classical design problems is the K irk m a n 's fifteen school girl problem(1850): Fifteen young ladies in a school walk out three abreast for seven days in succession; it is required to arrange them daily, so that 1