Timeline for Exact bin packing the harmonic series: references?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 3, 2017 at 18:49 | comment | added | Gerhard Paseman | This gets a vote up from me. Gerhard "That Might Be My Tenth" Paseman, 2017.03.03. | |
| Mar 3, 2017 at 18:47 | vote | accept | Gerhard Paseman | ||
| Feb 28, 2017 at 20:42 | comment | added | Gerhard Paseman | If you are sufficiently computationally ambitious, here is what may be a tractable subtask. Given n and E_n = B_n - 1, the number of bins to pack exactly, let G_p be the subset of unit fractions with p smooth denominators. Bump up p until the sum over G_p exceeds E_n, and then see if the difference is expressible as a sum of a subset of G_p. When it is, you have a trial set for exact packing, or possibly a short proof that it can't be done. Gerhard "May Compute Ambitiously Later Today" Paseman, 2017.02.28. | |
| Feb 28, 2017 at 20:25 | comment | added | Gerhard Paseman | Also, you have quite a few smooth numbers as denominators. Perhaps an estimate as to how many sevenses or elevenses are needed may give a clue? Gerhard "Happy Birthday To My Dad" Paseman, 2017.02.28. | |
| Feb 28, 2017 at 20:21 | comment | added | Gerhard Paseman | Wow! I didn't think you could find this! Dare to conjecture if there are any more, or how soon we can exactly pack the next bin? Gerhard "Go On, I Dare You" Paseman, 2017.02.28. | |
| Feb 28, 2017 at 19:51 | history | answered | Jeremy Rouse | CC BY-SA 3.0 |