Neil J. A. Sloane: Home Page

• AT&T Fellow
  Address: AT&T Shannon Lab, 180 Park Ave, Room C233, Florham Park NJ 07932-0971 USA
  Voice: 973 360 8415, Fax: 973 360 8178. Email: njas@research.att.com
  (An alternative address, which however I do not check very often, is njasloane@gmail.com)

  [ Last modified Sat Jul 31 00:23:06 EDT 2010 ]

• Recent changes to these pages
  • The On-Line Encyclopedia of Integer Sequences receives thousands of hits each day. Contains 177924 sequences [Sat Jul 31 00:23:06 EDT 2010]
  • N. J. A. Sloane, Vinay A. Vaishampayan and Sueli I. R. Costa, A Note on Projecting the Cubic Lattice [April 5, 2010; revised April 24 2010, May 25 2010, Jul 14 2010.]
  • David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Feb 11 2010, revised Apr 21 2010.
  • The OEIS Movie! To celebrate the launching of the OEIS Foundation, Tony Noe has made a movie showing the first 1000 terms of 1000 sequences, with soundtrack from Recaman's sequence A005132. The best way to watch it is to first download the file from Tony's web site, http://www.sspectra.com/math/OEISMovie.mov and then play it with QuickTimePlayer 7.
  • N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS, Jan 09 2010.
  • Benjamin Chaffin and N. J. A. Sloane, The Curling Number Conjecture, preprint. [Dec 11 2009, revised Feb 13 2010]
  • The OEIS Foundation is now set up. It exists to own, maintain and collect funds to support the On-Line Encyclopedia of Integer Sequences. The Foundation is a 501(c)(3) tax-exempt organization. For more information see the OEIS Foundation web site. See especially the poster and the press release. [Nov 19 2009]
  • Challenge Problems: Independent Sets in Graphs [May 7 2001; revised July 2003, Sept. 2003, May 15 2005, Oct 24 2009, Nov 18 2009]
  • David Applegate and N. J. A. Sloane, The Gift Exchange Problem, arXiv:0907.0513, slightly later version with typo corrected. [Jul 02 2009]
  • Podcast of me being interviewed by Chaim Goodman-Strauss about the On-Line Encyclopedia of Integer Sequences. (Part of the MAA Math Factor Podcast series.)
  • Eight Hateful Sequences, short paper for the 8th Gathering for Gardner [pdf]. [May 13 2008]
  • I have updated the list of papers that reference the OEIS: there are now over 1700 items. [Dec 01 2009]
  • N. J. A. Sloane and Vinay A. Vaishampayan, Generalizations of Schöbi's Tetrahedral Dissection [pdf]. [Oct 20 2007, Oct 22 2007, Nov 13 2007, May 13 2008]
  • Chao Tian, Vinay A. Vaishampayan and N. J. A. Sloane, Constant Weight Codes: A Geometric Approach Based on Dissections [pdf]. [Jun 08 2007]
  • Nice Poster for talk about the OEIS I gave at MIT on Apr 30 2007. [The original is on the MIT Applied Math Colloquium web site. The poster was brilliantly executed by Shirley A. Entzminger of MIT from a crude rough draft that I sent her.]
  • Index to my coauthors [Nov 16 2006]
  • J. H. Conway and N. J. A. Sloane, The Optimal Isodual Lattice Quantizer in Three Dimensions [pdf, ps]. [Jan 02 2007]
  • David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing [pdf]. [Nov 09 2006, Feb 07 2007, Aug 28 2007, Sep 25 2007]
  • David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons, Proposed problem for American Math. Monthly [pdf, ps]. [Oct 10 2006]
  • Gleason's theorem on self-dual codes and its generalizations (talk given at Conference on Algebraic Combinatorics in honor of Eiichi Bannai, Sendai, Japan, June 2006, and based on the new book, Self-Dual Codes and Invariant Theory, by G. Nebe, E. M. Rains and N. J. A. Sloane, Springer, Berlin, published Feb 06 2006).
  • N. J. A. Sloane and Parthasarathy Nambi, Integer Sequences Related to Chemistry [pdf], Poster to be presented at the Amer. Chem. Soc. National Meeting, San Francisco, Fall 2006 [Aug 14, 2006]
  • Seven Staggering Sequences [pdf], based on talk given at 7th Gathering for Gardner, Atlanta, March 2006. [Apr 14, 2006]
  • Notes on 7th Gathering for Gardner [May 15, 2006]
  • The new book is out! Self-Dual Codes and Invariant Theory, by G. Nebe, E. M. Rains and N. J. A. Sloane, Springer, Berlin, published Feb 06 2006.
  • New: I have reopened the doors to the 100K sequence e-party! Click here to join. [Jan 28 2006]
  • Nadia Heninger, Eric Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions [pdf, ps]. [Aug 26, 2005; revised Nov 10, 2005, Apr 08 2006]
  • Fokko J. van de Bult, Dion C. Gijswijt, John P. Linderman, N. J. A. Sloane and Allan R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps]. [Jun 26 2004; latest revision Sep 16 2006]
  • David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping Binary Numbers: A New Sequence Related to the Binary Numbers [pdf, ps]. [Apr 19 2005; revised Jul 26 2005]
  • Di Cook's movie of the olive oil data. This displays a certain 8-dimensional dataset by projecting it onto a sequence of 40 planes in 8-space that were obtained from the E_8 lattice (one of our Grassmannian packings). Requires a QuickTime viewer.
  • N. J. A. Sloane and J. A. Sellers, On Non-Squashing Partitions (arXiv: math.CO/0312418) [Dec 19 2003]
  • F. E. Oggier, N. J. A. Sloane, A. R. Calderbank and S. N. Diggavi, Nonintersecting Subspaces Based on Finite Alphabets [pdf, ps] [Dec 15, 2003]
  • G. Nebe, H.-G. Quebbemann, E. M. Rains and N. J. A. Sloane, Complete Weight Enumerators of Generalized Doubly-Even Self-Dual Codes (arXiv: math.NT/0311289) [Nov 15, 2003]
  • Brendan D. McKay, Frederique E. Oggier, Gordon F. Royle, N. J. A. Sloane, Ian M. Wanless and Herbert S. Wilf, Acyclic digraphs and eigenvalues of (0,1)-matrices (arXiv: math.CO/0310423) [Oct 24, 2003]
  • G. Nebe, E. M. Rains and N. J. A. Sloane, Codes and Invariant Theory (arXiv: math.NT/0311046) [Jan 01 2003, revised Oct 06 2003]
  • Review of George Szpiro's book Kepler's Conjecture: How some of the greatest minds in history helped solve one of the oldest math problems in the world (Wiley), Nature, 11 Sept. 2003 (Vol. 425, No. 6954), pp. 126-127 [pdf, ps].
  • J. C. Lagarias and N. J. A. Sloane, Approximate Squaring (arXiv: math.NT/0309389) [Aug 13, 2003; revised Sep 08, 2003]
  • N. J. A. Sloane and T. Wieder, The Number of Hierarchical Orderings (arXiv: math.CO/0307064) [Jul 04 2003]
  • The On-Line Encyclopedia of Integer Sequences was featured in Ivars Peterson's MathTrek in Science News Online for May 17, 2003.
  • Gosset has been recompiled to remove some minor bugs. [May 07, 2003]
  • Handout (pdf or ps) for "Take Our Children To Work" day, with some puzzles to illustrate the On-Line Encyclopedia of Integer Sequences [Apr 26 2003]
  • B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical Analogues of Aronson's Sequence (arXiv: math.NT/0305308) [Mar 28 2003]
  • The On-Line Encyclopedia of Integer Sequences, Notices Amer. Math. Soc., Sept. 2003.
  • Spherical Designs in Four Dimensions (Extended Abstract) (with R. H. Hardin and P. Cara), [Abstract, pdf, postscript]. [Feb 16 2003]
  • Added (a) translations of the Encyclopedia lookup page into many languages (see also the translation page), (b) many orthogonal arrays to the OA library, (b) new sequence tranformations to the transforms file, (c) many recent papers of mine to the LANL e-print arXiv, (d) many older papers to this web site. [Oct 04, 2002]

  • Jeffrey Shallit has agreed to take over the editorship of the electronic Journal of Integer Sequences. which I founded four years ago. The link points to its new home page. [Apr 14, 2002]
  • D. Applegate, E. M. Rains and N. J. A. Sloane, On Asymmetric Coverings and Covering Numbers (arXiv: math.CO/0205303) [May 28 2002]
  • J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG Sequence (arXiv: math.NT/0204011) [Mar 11, 2002]
  • Construction of multiple description vector quantizers. [Dec 23 2001]
  • Electronic versions of many old papers are being added to my web pages -- see my publication list for details. This is an on-going project.
  • Integer Sequences WebCam! [Jun 08 2001]

  • Claude Shannon (1916-2001), draft of article that appeared in Nature (with Robert Calderbank) [April 6, 2001]
  • List of things that need to be done for the On-Line Encyclopedia of Integer Sequences, in case anyone wants to help! [Apr 18, 2001]
  • Sequences in classic books: Comtet's Advanced Combinatorics, Harary and Palmer's Graphical Enumeration, Stanley's Enumerative Combinatorics. [Feb 1, 2001]
  • Interleaver design for turbo codes [Nov 8 2000]
  • The database of packings, coverings and max volume arrangements of from 60 to 78032 points on a sphere with icosahedral symmetry has been revised to make it easy to download the points. [Oct 24 2000]
  • A Simple Construction for the Barnes-Wall Lattices (with Gabriele Nebe and Eric Rains) [Abstract, pdf, postscript]. [July 6, 2000]
  • NEW! Rock Climbing Guide New Jersey (with Paul Nick) [June 2, 2000]
  • On Single-Deletion-Correcting Codes [Abstract, pdf, postscript]. [Feb. 21, 2001]
  • Many Spherical codes (arrangements of points on spheres in various dimensions) have been added - see the section on Tables below. [June 13, 2000]
  • The Invariants of the Clifford Groups (with Gabriele Nebe and Eric Rains) [Abstract, pdf, postscript]. [Sept 8, 2000]
  • The Lattice of N-Run Orthogonal Arrays (with Eric Rains and John Stufken) [Abstract, pdf, postscript]. [Apr 14, 2000]
  • My Favorite Integer Sequences, a paper for the SETA'98 conference on sequences [Abstract, pdf, postscript, latex] [revised Jan 19, 2001]. Also an article about the On-Line Encyclopedia for the forthcoming Handbook of Computer Science [pdf, postscript].
  • Orthogonal Arrays: Theory and Applications (book with Sam Hedayat and John Stufken). [May 15, 2002]
  • Packing Planes in Four Dimensions and Other Mysteries [pdf, postscript] (Talk on packings in Grassmannian spaces and error-correcting codes for quantum computers, based on 5 papers: (1), (2), (3), (4), (5). See also (6), (7).)
  • Tables of A(n,d), largest binary code of length n and minimal distance d (with Simon Litsyn and Eric Rains); and A(n,d,w), largest binary code of length n, distance d and constant weight w (with Eric Rains) [Apr 4 1999].
  • Sphere Packings, Lattices and Groups: the third edition of my book with John Conway appeared in 1998. The Preface to the Third edition [pdf, postscript] can be seen here. [June 13 2000].
  • Note on optimal unimodular lattices [pdf, postscript] (with J.H. Conway): shows among other things that there are precisely 5 odd optimal unimodular lattices in 32 dimensions, but more than 8*10²⁰ in dimension 33. [Feb 10 1998]
  • Shadow theory of modular and unimodular lattices (with Eric Rains): new bounds for unimodular and N-modular lattices. [Apr 27 1998]
  • Catalogue of Lattices. New: table of kissing numbers. [Sep 14 1999]
  • Robert Calderbank's interview with me appeared in the IEEE Information Theory Society Newsletter.
  • The Calderbank-Rains-Shor-Sloane paper on Quantum error correction via codes over GF(4) [pdf, postscript].
  • Self-dual codes [pdf, postscript] A long survey article written with Eric Rains for the Handbook of Coding Theory [May 19 1998].
  • Eternal (or Perpetual) Home Page Proposal. Revised 1997 (Related links).
  • Mixed binary-ternary codes [pdf, postscript]: Suppose you want a set of vectors in which the first b coordinates are binary and the last t coordinates are ternary, and you want Hamming distance at least d between any two vectors. How many vectors can you have? This paper gives bounds, constructions and extensive tables -- including a table of pure ternary codes that is better than any previous table.
  • Quantum error-correcting codes
  • Packing lines, planes, etc.: packings in Grassmannian spaces,
  • Codes over Z4
  • Coordination sequences -- see also these two papers, which deal with the coordination sequences of crystal structures, especially zeolites and of lattices [pdf, postscript]
  • Spherical designs
  • See also the tail end of my publication list

• The Catalogue of Lattices. This data-base of lattices is a joint project with Gabriele Nebe, University of Aachen Our aim is to give information about all the interesting lattices in "low" dimensions (and to provide them with a "home page"). The data-base now contains about 125,000 lattices.
• Gosset: An extremely powerful general-purpose program for constructing experimental designs developed by R. H. Hardin and me over the past seven or so years. Available for beta-testing. Runs under Unix or Linux. [Aug 28 2001].
• Tables
  • The Catalogue of Lattices
  • Integer Sequences
  • Spherical codes (packings) [updated June 13 2000]
  • Spherical codes (packings, coverings and max volume arrangements with icosahedral symmetry) [updated Oct 24, 2000]
  • Spherical codes (coverings)
  • Spherical codes (t-designs)
  • Spherical codes (minimal potential energy arrangements)
  • Spherical codes (maximal volume arrangements)
  • Packings of lines, planes etc.: packings in Grassmannian space
  • Minimal-energy clusters of hard spheres
  • Minimal Lennard-Jones potential clusters of soft spheres
  • Linear and nonlinear codes; including a table (maintained with Simon Litsyn and Eric Rains) of the best such codes.
  • Constant weight codes This page is now obsolete! It is superseded by Andries Brouwer's table.
  • Experimental designs (under construction)
  • Hadamard matrices
  • Orthogonal Arrays:
    (a) Parameters of arrays with up to 100 runs
    (b) Library of explicit arrays
    (c) The book.
  • Isometric embeddings of one space in another (no link yet)
• Papers and Books Grouped by Subject:
  • coding theory (see also covering radius of codes and codes over Z4),
  • sphere packing, lattices and quadratic forms
  • packing lines, planes, etc.: packings in Grassmannian spaces,
  • spherical codes and designs,
  • quantizing,
  • geometry,
  • combinatorics,
  • designs (including experimental designs) (see also Gosset),
  • integer sequences,
  • group theory,
  • graph theory,
  • spectroscopy,
  • crystallography,
  • cryptography,
  • rock climbing

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