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Abstract
Given positive integers e_{1}, e_{2} , let X_{i} denote the set of e_{i} dimensional subspaces of a fixed finite vector space V=(Fq)e1+e2 . Let Y_{i} be a nonempty subset of X_{i} and let α_{i}=  Y_{i} /  X_{i} . We give a positive lower bound, depending only on α_{1}, α_{2}, e_{1}, e_{2}, q , for the proportion of pairs (S_{1}, S_{2}) ∈ Y_{1}× Y_{2} which intersect trivially. As an application, we bound the proportion of pairs of nondegenerate subspaces of complementary dimensions in a finite classical space that intersect trivially. This problem is motivated by an algorithm for recognizing classical groups. By using techniques from algebraic graph theory, we are able to handle orthogonal groups over the field of order 2, a case which had eluded Niemeyer, Praeger, and the first author.
Original language  English 

Pages (fromto)  28792891 
Number of pages  13 
Journal  Designs, Codes, and Cryptography 
Volume  91 
Issue number  9 
DOIs  
Publication status  Published  Sept 2023 
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Dive into the research topics of 'The proportion of nondegenerate complementary subspaces in classical spaces'. Together they form a unique fingerprint.Projects
 1 Finished

Complexity of group algorithms and statistical fingerprints of groups
Praeger, C. & Niemeyer, A.
ARC Australian Research Council
21/02/19 → 31/12/22
Project: Research