Equivalence classes of Latin squares and nets in CP^2

Details Equivalence classes of Latin squares and nets in CP^2 Equivalence classes of Latin squares and nets in CP^2

2007-03-06

arxiv.org/abs/math/0703142v4

Mathematics

Combinatorics

14 pages

Scientific paper

The fundamental combinatorial structure of a net in CP^2 is its associated set of mutually orthogonal latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in CP^2. Then we count these equivalence classes for small cases. Finally, we prove that the realization spaces of these classes in CP^2 are empty to show some non-existence results for 4-nets in CP^2.

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