| Abstrakt: |
In this article we generalize the concepts that were used in the PhD thesis of Drudge to classify Cameron–Liebler line classes in PG (n , q) , n ≥ 3 , to Cameron–Liebler sets of k-spaces in PG (n , q) and AG (n , q) . In his PhD thesis, Drudge proved that every Cameron–Liebler line class in PG (n , q) intersects every 3-dimensional subspace in a Cameron–Liebler line class in that subspace. We are using the generalization of this result for sets of k-spaces in PG (n , q) and AG (n , q) . Together with a basic counting argument this gives a very strong non-existence condition, n ≥ 3 k + 3 . This condition can also be improved for k-sets in AG (n , q) , with n ≥ 2 k + 2 . [ABSTRACT FROM AUTHOR] |
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