Timeline for Flooding a cycle digraph via chip-firing: $n^{k-1} + n^{k-2} + \cdots + 1$ bound (a Norway 1998-99 problem generalized)
Current License: CC BY-SA 3.0
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| Jan 17, 2017 at 0:38 | history | edited | darij grinberg | CC BY-SA 3.0 |
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| Feb 28, 2015 at 15:34 | comment | added | darij grinberg | This is an even better proof. Thanks a lot! | |
| Feb 28, 2015 at 15:32 | vote | accept | darij grinberg | ||
| Feb 28, 2015 at 12:11 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
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| Feb 28, 2015 at 12:04 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
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| Feb 28, 2015 at 11:31 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
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| Feb 28, 2015 at 11:10 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
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| Feb 28, 2015 at 10:24 | comment | added | Fedor Petrov | @darij I edited the post with conjecture 2 included, please check as the proof looks to easy. | |
| Feb 28, 2015 at 10:23 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
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| Feb 28, 2015 at 0:24 | comment | added | darij grinberg | I was merely stating the lemma to make the proof more readable to others. It is very close to (but probably not easily derived from) Theorem 2.1 in ams.org/journals/tran/1956-082-02/S0002-9947-1956-0079851-X and what people call "cycle lemma". | |
| Feb 28, 2015 at 0:04 | comment | added | Fedor Petrov | @darij yes, I know the statement of the lemma (some brutal people do not need this for using lemmas, but I do), what I forgot is its name. Dini's lemma, or Rini, like that. | |
| Feb 27, 2015 at 22:40 | comment | added | darij grinberg | Very nice argument! I had been looking for something like this but did not see a good way to apply the lemma. Do you have an idea whether something like this applies to Conjecture 2 as well? | |
| Feb 27, 2015 at 22:39 | history | edited | darij grinberg | CC BY-SA 3.0 |
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| Feb 27, 2015 at 22:34 | comment | added | darij grinberg | Oh, you mean the lemma that allows you to make the WLOG assumption? That's the lemma that if you have $k$ reals $g_1, g_2, \ldots, g_k$ whose sum is $\geq 0$, then there exists some $r \in \left\{1,2,\ldots,k\right\}$ such that for every $s \in \left\{1,2,\ldots,k\right\}$, the sum $g_r + g_{r+1} + \cdots + g_{r+s-1}$ (where $g_i$ means $g_{i-k}$ if $i > k$) is $\geq 0$. | |
| Feb 27, 2015 at 22:33 | comment | added | darij grinberg | "I forgot how is this lemma called": it's (an easy consequence of) Bernoulli's inequality. (Still reading your post.) | |
| Feb 27, 2015 at 22:02 | history | answered | Fedor Petrov | CC BY-SA 3.0 |