Saaty, T.L., Kainen, P.C.: The Four-Color Problem: Assaults amd Conquest. New York: McGraw-Hill, 1977. Home/Search Document Not in Database Summary Related Articles Check |
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The still-Life density problem and its generalizations - Noam Elkies June (1998) (1 citation) (Correct)
....values 3=5 and 9=13 on ffi(n) are correct then no finite N will suffice to prove them. More recently (Dec. 95) Marcus Moore announced on the usenet newsgroup comp.theory.cell automata a new approach to bounding ffi(n) from above, closely related to discharging arguments as explained in [6] (thanks to Allan Wechsler for this reference) In that forum, and in later personal communication [4] Moore claims a simpler proof of ffi(3) 1=2, as well as the new results ffi(5) 9=13 and ffi(4) 6 8=13. To my knowledge these results have yet to appear even in preprint form. 4. Proof of ....
....this case the Voronoi cell of (0; 1) 2 S must have area at least 11=4. In general we shall see that S can be partitioned into uniformly bounded subsets S 0 on which A x averages to at least 2. This method is thus also related, though more loosely than Moore s, with the discharging techniques of [6]: it can be regarded as reapportioning the A x locally to normalized cell areas A x 2 8 Z which still average to the inverse density of S but satisfy A x 2 for all x. The method is even more strongly reminiscent of Hsiang s approach to Kepler s conjecture, though fortunately not as many ....
Saaty, T.L., Kainen, P.C.: The Four-Color Problem: Assaults amd Conquest. New York: McGraw-Hill, 1977.
The still-Life density problem and its generalizations - Elkies (1997) (1 citation) (Correct)
....values 3=5 and 9=13 on ffi(n) are correct then no finite N will suffice to prove them. More recently (Dec. 95) Marcus Moore announced on the usenet newsgroup comp.theory.cell automata a new approach to bounding ffi(n) from above, closely related to discharging arguments as explained in [6] (thanks to Allan Wechsler for this reference) In that forum, and in later personal communication [4] Moore claims a simpler proof of ffi(3) 1=2, as well as the new results ffi(5) 9=13 and ffi(4) 6 8=13. To my knowledge these results have yet to appear even in preprint form. 4. Proof of ....
....case the Voronoi cell of (0; 1) 2 S must have area at least 11=4. In general we shall see that S can be partitioned into uniformly bounded subsets S 0 on which A x averages to at least 2. This method is thus also related, though more loosely than Moore s, with the discharging techniques of [6]: it can be regarded as reapportioning the A x locally to normalized cell areas A 0 x 2 1 8 Z which still average to the inverse density of S but satisfy A 0 x 2 for all x. The method is even more strongly reminiscent of Hsiang s approach to Kepler s conjecture, though fortunately not as ....
Saaty, T.L., Kainen, P.C.: The Four-Color Problem: Assaults amd Conquest. New York: McGraw-Hill, 1977.
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