Symmetries of the CM model, idempotents. Part V
Let us continue our analysis. Returning to table B, we note that the appearance of the bottom pair of lines has already been considered and explained. Let us deal with the top pair of bordering lines with numbers
XO = 120 with KVV = 554 And XO = 121 s KVV = 795. Lines with such KVV belong to the border of the dividing line of idempotents (layer 52) XO = 293 with KVV = 795 And XO = 396 with KVV = 554 between them 2 · 52 = 104 lines. Duplicate lines of these lines are “glued” together by the mechanism of generating duplicates into adjacent ones.
On the other hand, the line adjacent to the line above XO = 122 with KVK = 49 is generated by the involution for which it lies in the 7th layer, and the next duplicate row (from the 2nd layer) is generated by the symmetries (7th layer) of the row with KVC = 4, XO = 389
Conclusion
Five mechanisms for generating different “axial” lines (lines) by symmetrical border lines are considered. These mechanisms implement different mappings of border lines into duplicate lines:
– zero (bottom) line of the model;
– the central line of the model;
– a string of non-trivial involutions;
– the dividing line of pairs of a quadruple of adjacent rows;
– a line separating the lines of idempotents;
– the lower “zero” row indicates the symmetry of the placement of the “axial” elements; the dividing lines of the quadruple of adjacent rows and the equidistance from the center of the row of non-trivial involutions and; the dividing lines of the rows of idempotents and the “zero” row
– the central line of the SMM places duplicate lines at a constant distance (half of an even involution) from one another;
– the row of non-trivial involutions places duplicate rows layer by layer in rows with squares from distributed centers: the 1st layer from the row with KVK=1, the second layer – from the row with KVK=4, the third – from the row with KVK=9, etc.;
– the dividing line of pairs of lines of the ChKSS also places duplicate lines in layers from different centers, which represent dividing lines (centers) of even intervals with boundaries that are multiples of different divisors of the modulus N;
– the dividing line of idempotent lines transforms the removed pairs of border lines into duplicate lines and makes them adjacent (“glues”), while bordering the lines with the CVC; or places the duplicate lines in even intervals, making them the central pair there.
