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On existence of A-primitive partitions
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It is proved that for any natural m there exists the least positive integer N=N<sub>q</sub>(m) such that for n>N there are no A-primitive partitions F<sup>n</sup><sub>q</sub> into q<sup>m</sup> affine subspaces of dimension n-m. Lower and upper bounds for N=N<sub>q</sub>(m) are obtained. The results of that of the same type are set for face tilings.
Keldysh Institute of Applied Mathematics
Title: On existence of A-primitive partitions
Description:
It is proved that for any natural m there exists the least positive integer N=N<sub>q</sub>(m) such that for n>N there are no A-primitive partitions F<sup>n</sup><sub>q</sub> into q<sup>m</sup> affine subspaces of dimension n-m.
Lower and upper bounds for N=N<sub>q</sub>(m) are obtained.
The results of that of the same type are set for face tilings.
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