cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A057608 Maximal size of binary code of length n that corrects one transposition (end-around transposition not included).

Original entry on oeis.org

1, 2, 3, 4, 8, 12, 20, 38, 63, 110, 196, 352
Offset: 0

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Author

N. J. A. Sloane, Oct 09 2000

Keywords

References

  • S. Butenko, P. Pardalos, I. Sergienko, V. P. Shylo and P. Stetsyuk, Estimating the size of correcting codes using extremal graph problems, Optimization, 227-243, Springer Optim. Appl., 32, Springer, New York, 2009.
  • N. J. A. Sloane, On single-deletion-correcting codes, in Codes and Designs (Columbus, OH, 2000), 273-291, Ohio State Univ. Math. Res. Inst. Publ., 10, de Gruyter, Berlin, 2002.

Links

Crossrefs

Cf. A057657, A000016, A057591, A010101. Row sums of A085684.

Extensions

a(9) = 110 from Butenko et al., Nov 28 2001 (see reference).
a(9) = 110 also from Ketan Narendra Patel (knpatel(AT)eecs.umich.edu), Apr 29 2002. Confirmed by N. J. A. Sloane, Jul 07 2003
a(10) >= 196 and a(11) >= 352 from Butenko et al., Nov 28 2001 (see reference).
a(10) = 196 found by N. J. A. Sloane, Jul 17 2003
a(11) = 352 proved by Brian Borchers (borchers(AT)nmt.edu), Oct 16 2009

A057591 Maximal size of binary code of length n that corrects 2 deletions.

Original entry on oeis.org

1, 1, 2, 2, 2, 4, 5, 7, 11, 16, 24
Offset: 1

Views

Author

N. J. A. Sloane, Oct 05 2000

Keywords

Comments

Comments from Pablo San Segundo, Dec 04 2015 (Start): The search for a maximal clique in the graph 2dc.2048 has now finished. The answer is 24 (which was already known to be a lower bound).
The total time was 16.4 days using a 20-core XEON with 128Gb. 18 cores out of the 20 were in fact used.
The solution was found by a strong heuristic algorithm during pre-processing (about 5s). The actual search time was used "only" to prove optimality. The actual maximum clique algorithm is our most recent variant based on infra-chromatic BBMCX, described here, but as yet unpublished: https://www.researchgate.net/profile/Pablo_San_Segundo
The project was carried out by Pablo San Segundo and Jorge Artieda, Polytechnic University of Madrid (UPM), Center of Automation and Robotics (CAR). Supported by National Grant DPI 2014-53525-C3-1-R (End)

Links

Crossrefs

Cf. A000016, A057608, A057657, A010101.

Extensions

Guenter Stertenbrink (Sterten(AT)aol.com) found a(9) = 11 and a(10) >= 16, Apr 28 2001
James B. Shearer (jbs(AT)pkmfgvm4.vnet.ibm.com) proved that a(10) = 16, Sep 20 2003
Pablo San Segundo and Jorge Artieda showed that a(11) = 24, Dec 04 2015

A085685 Triangle read by rows: T(n,k), n >= 0, 0 <= k <= n, is size of maximal 1-transposition-correcting code formed using binary vectors of length n and weight k. The end-around transposition is allowed.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 3, 6, 3, 2, 1, 1, 2, 4, 7, 7, 4, 2, 1, 1, 2, 6, 10, 12, 10, 6, 2, 1, 1, 3, 7, 18, 21, 21, 18, 7, 3, 1, 1, 3, 9, 21, 33, 37, 33, 21, 9, 3, 1, 1, 3, 11, 28, 52, 63, 63, 52, 28, 11, 3, 1
Offset: 0

Views

Author

N. J. A. Sloane, Jul 17 2003

Keywords

Examples

			Triangle begins
1
1 1
1 1 1
1 1 1 1
1 1 1 1 1
1 1 2 2 1 1

Links

Crossrefs

Row sums are A057657.

Extensions

Row 10 from Brian Borchers (borchers(AT)nmt.edu), Apr 14 2005
Row 11 from Brian Borchers (borchers(AT)nmt.edu), Nov 04 2009
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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