ISSN:
1420-8997
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In some projective spaces the complement of a simplex can be partitioned into disjoint copies of a higher or lower dimensional projective space of a different order. More precisely, let d and e be positive integers with e ≥ 2. We exhibit an embedding of PG(d,q) in PG(e,qd+1) and show that the complement of a simplex in PG(e,qd+1) may be partitioned into disjoint copies of embedded PG(d,q)'s, Each embedded PG(d,q) spans PG(e,qd+1) whenever d ≥ e. These results are also true for PG(d,F) and PG(e,K) for infinite fields $$F \subseteq K$$ for which degF K=d+1 and the field extension is normal, separable, and cyclic.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01230599
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