Timeline for What does the generating function $x/(1 - e^{-x})$ count?
Current License: CC BY-SA 3.0
33 events
| when toggle format | what | by | license | comment | |
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| Aug 4, 2019 at 22:58 | answer | added | Tom Copeland | timeline score: 0 | |
| Oct 1, 2015 at 5:06 | comment | added | Tom Copeland | It's interesting to see how a question assumes a life of its own. How many answers actualy address the question in the title or diagrammatics in the motivation section? | |
| Sep 28, 2015 at 18:50 | comment | added | Tom Copeland | There's are connections among folded 4-g-gons, Riemann zeta, and volumes of Riemann surfaces calculated by Witten as noted at the end of my last 'answer' . Look at a comment to the linked question about a paper by Lisa Jeffrey and see Jonah Sinick's answer there also. | |
| Sep 28, 2015 at 8:10 | answer | added | user21574 | timeline score: 2 | |
| Sep 2, 2015 at 4:13 | answer | added | Theo Johnson-Freyd | timeline score: 4 | |
| Sep 2, 2015 at 2:51 | comment | added | Theo Johnson-Freyd | @TomCopeland I don't know how to answer the question my six-years-ago self was asking, but I did have a new insight into these diagrammatics, which I will try to explain in an answer (far) below, if you're curious. | |
| Sep 2, 2015 at 2:51 | comment | added | Theo Johnson-Freyd | ... seen as cubes with some faces collapsed. I mean, if you write the multiplication as an arrow (which it is) instead of a vertex, then an associator fills in a square. The pentagonator fills in a 3-cube, five of whose faces are the associators in the usual pentagon, but one face is the fact that $((ab))(cd) = (ab)((cd))$. Etc. I don't know, though, if those cubes are actually related to this problem. | |
| Sep 2, 2015 at 2:47 | comment | added | Theo Johnson-Freyd | @ScottCarter Almost six years later, I realize I still never answered your question, and only realized that when Tom Copeland left his comment. I don't have any drawings at hand, and honestly don't remember how I came to that description, although I do remember thinking about it carefully. Probably it's an unpacking of some known combinatorics of BCH series from Wikipedia? Looking over it, the fact that arrows go to the right reminds me of the "Wick formula" for time ordered versus star products. The only connection to cubes that I can come up with off hand is that associahedra can be ... | |
| Sep 2, 2015 at 0:15 | comment | added | Tom Copeland | Theo, it's been a while. Any new insights on the diagrammatics? Surjections a la permutohedra and reciprocal e.g.f.s, and non-crossing partitions and Dyck paths via compositional inversion are related. @Scott Carter, hypercubes are related--see the H&S ref in my answer. | |
| Aug 31, 2015 at 14:38 | history | edited | user9072 | CC BY-SA 3.0 |
fixed broken stars
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| Aug 31, 2015 at 14:25 | answer | added | Joe Silverman | timeline score: 9 | |
| Aug 31, 2015 at 12:01 | answer | added | Anixx | timeline score: 0 | |
| Nov 20, 2014 at 21:45 | answer | added | Tom Copeland | timeline score: 6 | |
| S Jun 27, 2014 at 19:54 | history | suggested | F. C. |
added the tag bernoulli-numbers, that was obviously missing
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| Jun 27, 2014 at 19:48 | review | Suggested edits | |||
| S Jun 27, 2014 at 19:54 | |||||
| Mar 9, 2010 at 9:06 | answer | added | Bruce Westbury | timeline score: 7 | |
| Feb 26, 2010 at 4:51 | comment | added | Allen Knutson | Another place to see this series, though shifted by two: the Planck black-body distribution. en.wikipedia.org/wiki/Planck's_law | |
| Feb 23, 2010 at 22:41 | answer | added | Jason Bandlow | timeline score: 7 | |
| Feb 23, 2010 at 16:24 | answer | added | David E Speyer | timeline score: 19 | |
| Feb 23, 2010 at 15:57 | answer | added | vonjd | timeline score: 3 | |
| Feb 23, 2010 at 15:37 | answer | added | Zoran Skoda | timeline score: 6 | |
| Jan 2, 2010 at 21:18 | answer | added | Emerton | timeline score: 22 | |
| Dec 18, 2009 at 15:29 | comment | added | Scott Carter | Do you have an explicit diagram drawn somewhere that explicates your penultimate paragraph? Since the Bernoulli numbers have something to do with summing $k\/$th powers, there should be a connection to this diagram and some decomposition of the $n$-cube. | |
| Dec 18, 2009 at 6:25 | answer | added | Kevin O'Bryant | timeline score: 24 | |
| Dec 18, 2009 at 6:22 | comment | added | Steve Huntsman | Given your background you might be interested to know that this power series is used to define the Todd class: en.wikipedia.org/wiki/Todd_class | |
| Dec 18, 2009 at 3:34 | answer | added | Tom Leinster | timeline score: 17 | |
| Dec 18, 2009 at 3:27 | comment | added | Michael Lugo | @Theo: I didn't actually remember these were the Bernoulli numbers until I did the expansion (by computer, of course) and saw the mysterious numerator 691. | |
| Dec 18, 2009 at 2:55 | comment | added | Theo Johnson-Freyd | @Qiaochu: See, I'm neither a combinatorialist nor a number theorist, and although I guess I've seen the Bernoulli numbers before, I never really encoded them in memory. Anyway, I've accepted Pete's answer below, but I'm secretly hoping that someone will connect it with the diagrams I described. | |
| Dec 18, 2009 at 2:52 | vote | accept | Theo Johnson-Freyd | ||
| Dec 18, 2009 at 2:46 | answer | added | Pete L. Clark | timeline score: 31 | |
| Dec 18, 2009 at 2:02 | answer | added | Michael Lugo | timeline score: 5 | |
| Dec 18, 2009 at 1:57 | comment | added | Qiaochu Yuan | I am sort of astonished that you gave so much background without mentioning the name of this sequence: en.wikipedia.org/wiki/Bernoulli_number | |
| Dec 18, 2009 at 1:44 | history | asked | Theo Johnson-Freyd | CC BY-SA 2.5 |