Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke





.......................

.......................


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 2022/01/23)

    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) ).

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320