Timeline for What alternatives are there to the binomial poset theory of generating function families?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Sep 30, 2022 at 20:08 | answer | added | geoffrey | timeline score: 3 | |
| S May 21, 2021 at 17:05 | history | bounty ended | CommunityBot | ||
| S May 21, 2021 at 17:05 | history | notice removed | CommunityBot | ||
| May 13, 2021 at 18:55 | answer | added | Richard Stanley | timeline score: 6 | |
| S May 13, 2021 at 15:32 | history | bounty started | Keshav Srinivasan | ||
| S May 13, 2021 at 15:32 | history | notice added | Keshav Srinivasan | Draw attention | |
| May 9, 2021 at 23:11 | comment | added | Timothy Chow | While not exactly an answer to your question, the umbral calculus can be regarded as an example of something that, as far as I know, isn't neatly subsumed by any of the the theories you mentioned. See for example Ira Gessel's Applications of the classical umbral calculus. | |
| May 9, 2021 at 21:14 | answer | added | Ira Gessel | timeline score: 5 | |
| May 9, 2021 at 17:40 | comment | added | Martin Rubey | @KeshavSrinivasan: note that also the Dirichlet generating function $\sum_n \frac{a_n}{n! n^s}$ found its way into combinatorial species, see Maia, Méndez, On the arithmetic product of combinatorial species. Furthermore there are analogues for the wreath product groups $Z_r\wr \mathfrak S_n$. But this doesn't answer your question. | |
| May 8, 2021 at 22:00 | comment | added | Keshav Srinivasan | @SamHopkins Yeah I saw that, but because he said “various aspects” I didn’t know if all of those answered the specific question of which families of generating functions are combinatorially useful, as opposed to merely addressing other aspects like the combinatorial meaning of generating function operations. Plus aren’t combinatorial species always used with exponential generating functions? | |
| May 8, 2021 at 21:57 | comment | added | Sam Hopkins | I would say yes about species. For example, in the notes at the end of Chapter 3 in EC1, Stanley writes: "Among the many alternative theories to binomial posets for unifying various aspects of enumerative combinatorics and generating functions, we mention the theory of prefabs of Bender and Goldman [3.7], dissects of Henle [3.42], linked sets of Gessel [3.31], and species of Joyal [3.44]. The most powerful of these theories is perhaps that of species, which is based on category theory." But someone more expert will probably answer... | |
| May 8, 2021 at 21:53 | history | asked | Keshav Srinivasan | CC BY-SA 4.0 |