Timeline for Meaning of a quote of Doubilet, Rota and Stanley on harmonic analysis and combinatorics
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Mar 24, 2022 at 18:51 | comment | added | Tom Copeland | Some notes for exploring some connections between Rota and probability theory are in the blog post "On the origin of moment-cumulant formulas" by Speicher (wordpress.com/read/blogs/155738873/posts/1080). For Laplace on this, see the article by Hald "The Early History of the Cumulants and the Gram-Charlier Series" mentioned in the post. | |
| Feb 17, 2022 at 13:35 | history | edited | Tom Copeland | CC BY-SA 4.0 |
included attribution of an article and link to further history of probability
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| Dec 24, 2021 at 11:42 | comment | added | Tom Copeland | The Stieltjes transform more precisely rather than the Cauchy transform, but formal moments and cumulants can be defined independent of any pdf. | |
| Oct 10, 2021 at 21:29 | history | edited | Tom Copeland | CC BY-SA 4.0 |
More notes on Rota, posets, and probability
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| Sep 12, 2021 at 21:44 | comment | added | Tom Copeland | Of historical interest: "Laplace's calculus of generatrix functions" by Irene Price and Section 7. The Generatrix Calculus (pg. 28 and on) of The Theory of The Theory of Linear Operators by Davis archive.org/details/theoryoflinearop033341mbp/page/n47/mode/… | |
| Apr 3, 2021 at 0:11 | comment | added | Gerry Myerson | See meta.mathoverflow.net/questions/3131/… and the links various users posted there to get the scoop on pinging, Tom. | |
| Apr 2, 2021 at 17:49 | comment | added | Tom Copeland | For the uninitiated, my blog post Squaring Triangles (tcjpn.wordpress.com/2019/09/04/squaring-triangles) gives two simple, fundamental, examples of the connections among generating functions, algebraic operations, recursion relations, and geometric combinatorics. There, of course, are differential equations related to this, as noted in the associated OEIS entries. | |
| Apr 2, 2021 at 11:51 | comment | added | Gerry Myerson | You can't ping someone who hasn't contributed to this answer, Tom. | |
| Apr 2, 2021 at 6:31 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Elaborated
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| Oct 13, 2020 at 4:24 | comment | added | Tom Copeland | For relation to free probability, moments, cumulants, see "Three lectures on free probability" by Novak and LaCroix arxiv.org/abs/1205.2097 (search therein for Rota and Stanley also). | |
| Jan 20, 2020 at 17:34 | comment | added | Tom Copeland | One could define a formal pdf by, say, taking the inverse Laplace transform of the e.g.f. $e^{-b.t}$. | |
| Jan 4, 2020 at 20:57 | comment | added | Tom Copeland | pdf = probability density function, not to be confused with the cumulative distribution en.m.wikipedia.org/wiki/Probability_density_function. See a relevant overview in intro of "An umbral setting for cumulants and factorial moments" by E. Di Nardo, D. Senato arxiv.org/abs/math/0412052 | |
| Dec 20, 2019 at 4:48 | history | edited | LSpice | CC BY-SA 4.0 |
TeX fixes, and link to Xia paper
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| Dec 19, 2019 at 22:02 | history | answered | Tom Copeland | CC BY-SA 4.0 |