## On the Construction of Latin Squares Counterbalanced for Immediate Sequential Effects |

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Algorithm II gives Alimena alphabet Appendix called cells chord CLS transformation set CLSs columns of Q(A),Q(M columns of R2 columnwise linear permutation construct by Algorithm counterbalanced for immediate cyclic Latin squares decreasing function definition diagonals Educational Psychology El>j Em+d(j En+m+q En+q Euler*s conjecture Exorcism follows that kc form a permutation Greco-Latin square immediate sequential effects k non-negative k types k-1 natural numbers k-a rows last a rows last c columns linear sets magic square mean separation mirror image mod.k modulo k Non-CLS Permutations Satisfying non-negative integers O(mod.k obtain orthogonal Latin squares orthogonal squares pairs of types permutation by rows Permutations Satisfying 13.2 reader can verify recoded and linearly recodlng rectangles reduced modulo row and column SFL(l SFLs six 5x5 SQCB Latin square square exists square having P(E squares counterbalanced subscripts super-square Theorem thesis Ti+m>J union of linear University of Wisconsin values Write P(F Zl SI 9