Mathematical entertainments

@article{Gale1995MathematicalE,
  title={Mathematical entertainments},
  author={David Gale and Sherman K. Stein},
  journal={The Mathematical Intelligencer},
  year={1995},
  volume={17},
  pages={37-39}
}
  • D. Gale, S. Stein
  • Published 1 March 1995
  • Mathematics
  • The Mathematical Intelligencer
7 Citations
The length of an s-increasing sequence of r-tuples
TLDR
A number of results related to a problem of Po-Shen Loh are proved, improving some of the known bounds, pointing out connections to other well-known problems in extremal combinatorics, and asking a number of further questions.
Orthogonal Polynomials in Information Theory
The following lectures are based on the works (Tamm, Communication complexity of sum-type functions, 1991, [115]; Appl Math Lett 7:39–44, 1994, [116]; Inf Comput 116(2):162–173, 1995, [117]; Tamm,
Reflections about a Single Checksum
TLDR
A single checksum for codes consisting of n integer components is investigated and if the errors are such that a single component ci is distorted to ci±ei, the analysis leads to equivalent group factorizations.
Group Factorizations and Information Theory
  • U. Tamm
  • Computer Science
    2007 Information Theory and Applications Workshop
  • 2007
TLDR
Group factorizations occur in the analysis of syndromes of integer codes, several graphs with large girth important for LDPC codes can be constructed using group factorizations, and various cryptosystems are based on them.
Packing tripods: Narrowing the density gap
Mathematics: What is the best way to lace your shoes?
TLDR
It is demonstrated mathematically that the shortest lacing is neither 'criss-cross' or 'straight' lacing, but instead is a rarely used and unexpected type of lacing known as 'bowtie' laces.
Tripods Do Not Pack Densely
TLDR
The second question in the negative is settled: the fraction of the space that can be filled with tripods of a growing size must be infinitely small.

References

Combinatorial packings of R3 by certain error spheres
TLDR
One of the "error spheres" discussed by Golomb in 1969, his "Stein corner" in three-dimensional Euclidean space R3 is concerned, and sufficiently dense packings are produced to show that they are much denser than the densest lattice packing.