Publications [#354207] of Benjamin Rossman

Papers Published

1. Rossman, B, Thresholds in the Lattice of Subspaces of Fqn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12118 LNCS (January, 2020), pp. 504-515, ISBN 9783030617912 [doi]
   (last updated on 2024/04/18)

   Abstract:
   Let Q be an ideal (downward-closed set) in the lattice of linear subspaces of Fqn, ordered by inclusion. For 0 ⩽ k⩽ n, let μk(Q) denote the fraction of k-dimensional subspaces that belong to Q. We show that these densities satisfyμk(Q)=11+z⟹μk+1(Q)⩽11+qz.This implies a sharp threshold theorem: if μk(Q) ⩽ 1 - ε, then μℓ(Q) ⩽ ε for ℓ= k+ O(logq(1 / ε) ).