Asymptotics of Random-Lattice Enumeration: Beyond HKZ via Dense Sublattices TCQ1JBR84Y

URI	`m2://res/TCQ1JBR84Y`
Kind	preprint
Creators	Thijs Laarhoven
Date	2026-10-11
Subjects	arxiv cs.CR, arxiv math.CO, arxiv math.MG
Scope	border

Expressions

Date	2026-10-11
Ids	arXiv 2610.15265

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
Deterministic HKZ prefix bound	statement	lemma 3	arxiv
Geometric bounds	statement	lemma 1	arxiv
A moment bound for the cumulative deficit	statement	lemma 4	arxiv
Few candidates are removed	statement	lemma 6	arxiv
Polynomial-space CVPP by collision search	statement	theorem 1.8	arxiv
Tree sizes of all quasi-HKZ bases	statement	theorem 1.1	arxiv
Completing the blocks	statement	lemma 9	arxiv
Dense sublattices with suitable blocks	statement	lemma 5	arxiv
Area rule	statement	proposition 4	arxiv
Averaging over primitive vectors	statement	proposition 1	arxiv
The reduced count has small variance	statement	lemma 7	arxiv
Tree size of recursive binary splits	statement	theorem 1.3	arxiv
Quasi-HKZ profiles on Haar-random lattices	statement	proposition 3	arxiv
Tree size of improved heuristic splits	statement	theorem 1.4	arxiv
Positive first moments for every subchain	statement	lemma 8	arxiv
Tree size from the prefix profile	statement	proposition 2	arxiv
FGL costs of a two-block split	statement	theorem 1.7	arxiv
Lower bound on the tree size	statement	theorem 1.5	arxiv
Averaging the two blocks of a split	statement	lemma 2	arxiv
Lower bound on the Feng--Gao--Liu cost factor	statement	theorem 1.6	arxiv
Tree size of a two-block split	statement	theorem 1.2	arxiv