The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Sphere Packings, Lattices and Groups.
Abstract
The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
On the Diagonalization of Quadratic Forms
Lam, T. Y. (1999) · Mathematics Magazine · doi:10.1080/0025570x.1999.11996736 · Cited by 8
Cited by
Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions
Andoni, A., & Indyk, P. (2008) · Communications of the ACM · doi:10.1145/1327452.1327494 · Cited by 1,437
Minimax and maximin distance designs
Johnson, M. E., Moore, L. M., & Ylvisaker, D. (1990) · Journal of Statistical Planning and Inference · doi:10.1016/0378-3758(90)90122-b · Cited by 1,451
Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions
Andoni, A., & Indyk, P. (2006) · 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06) · doi:10.1109/focs.2006.49 · Cited by 1,067
Minimum complexity density estimation
Barron, A. R., & Cover, T. M. (1991) · IEEE Transactions on Information Theory · doi:10.1109/18.86996 · Cited by 497
Scalar costa scheme for information embedding
Eggers, J. J., Bauml, R., Tzschoppe, R., & Girod, B. (2003) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2003.809366 · Cited by 357
Metadata
- Authors
- Coxeter, H. S. M., Conway, J. H., & Sloane, N. J. A.
- Venue
- The American Mathematical Monthly
- Publisher
- JSTOR
- Published
- 1989-06
- Volume
- 96
- Issue
- 6
- Pages
- 538
- ISSN
- 0002-9890 (ISSN-L)
- OpenAlex
- W1995990042
- Cited by
- 3,377
- References
- 1
- FWCI
- 45.33
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Sphere Packings, Lattices and Groups. https://app.cochat.ai/papers/10.2307/2323992
- The paper
- Coxeter, H. S. M., Conway, J. H., & Sloane, N. J. A. (1989). Sphere Packings, Lattices and Groups. The American Mathematical Monthly. https://doi.org/10.2307/2323992
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
