Constructions Of Magic Squares

Magic square can be traced back more than 4,000 years to "Luo Shu".Magic square is one of the combination design of the object of study.And magic square have important applications[31]in artificial intelligence,arts and crafts,electronic circuit principle of image information processing technology,etc.A lot of work has been done on the magic square[1,7-9].The first person to study the magic formula is Yang hui,the ancient Chinese mathematician.Yang hui has given an MS(8),which has a special property.In the reference literature,it is defined as the Yang hui type magic square labelparital result[18].While the magic rectangles are a natural generalization of magic square,which have long intrigued mathematicians and the general public.Harmuth studied magic rectangles over a century ago[19,20].In the recent past,N.Cao,K.Chen,Y.Zhang et al.gave some new results.In 2015,N.Cao,K.Chen,Y.Zhang studied the recursive structure of Yang hui type magic square[17]to construct a higher order number of Yang hui magic square.In 2014,Y.Zhang,K.Chen,N.Cao,H.Zhang used the strongly symmetric self-orthogonal diagonal Latin square to construct a YMS(n,2)[4],which contributed to the construction of the higher power of Yang hui's magic square.In 2013,Y.Zhang,J.Lei studied the method of constructing MR(mp,mq,2),m>3 and m in odd ways with MR(p,q,2)[23.The structure of this paper is as follows:In chapter 1,the basic concepts and symbols are briefly introduced;In chapter 2,we give the method of recursive structure of a magic square and Yang hui type magic square;In chapter 3,the author gives the construction method of multiple Yang hui type magic square,and constructs some new Yang hui type magic square;In chapter 4,we give MR(p,q,2)to construct MR(mp,mq,2),and the partial construction result of m as even;In chapter 5,we summarize the work done.