Thresholds in the Lattice of Subspaces of Fqn
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, Conference
Rossman, B
Published in: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
January 1, 2020
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) ).
Duke Scholars
Published In
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
DOI
EISSN
1611-3349
ISSN
0302-9743
Publication Date
January 1, 2020
Volume
12118 LNCS
Start / End Page
504 / 515
Related Subject Headings
- Artificial Intelligence & Image Processing
- 46 Information and computing sciences
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Rossman, B. (2020). Thresholds in the Lattice of Subspaces of Fqn. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12118 LNCS, pp. 504–515). https://doi.org/10.1007/978-3-030-61792-9_40
Rossman, B. “Thresholds in the Lattice of Subspaces of Fqn.” In Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 12118 LNCS:504–15, 2020. https://doi.org/10.1007/978-3-030-61792-9_40.
Rossman B. Thresholds in the Lattice of Subspaces of Fqn. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 2020. p. 504–15.
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, 2020, pp. 504–15. Scopus, doi:10.1007/978-3-030-61792-9_40.
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). 2020. p. 504–515.
Published In
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
DOI
EISSN
1611-3349
ISSN
0302-9743
Publication Date
January 1, 2020
Volume
12118 LNCS
Start / End Page
504 / 515
Related Subject Headings
- Artificial Intelligence & Image Processing
- 46 Information and computing sciences