Timeline for Integer-valued polynomials from Pólya counting
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 3, 2022 at 13:26 | vote | accept | Sam Hopkins | ||
| Jan 31, 2022 at 23:21 | comment | added | Sam Hopkins | @RichardStanley: Thank you for the reference! | |
| Jan 31, 2022 at 23:16 | comment | added | Richard Stanley | @SamHopkins: this is essentially what appears in Section 5.3 of Combinatorics: The Rota Way by Kung, Rota, and Yan. | |
| Jan 31, 2022 at 22:51 | comment | added | Sam Hopkins | This does make me wonder if there is a way to understand the basic Pólya counting results in terms of the quotient of the ordered partition lattice by $G$, and maybe Möbius inversion on this poset... | |
| Jan 31, 2022 at 18:28 | comment | added | Nate | @darijgrinberg Oh yea, good point. | |
| Jan 31, 2022 at 18:24 | comment | added | darij grinberg | @Nate I don't think that expansion has integer coefficients always. $a_j$ is not necessarily a multiple of $j!$. You get some kind of non-freeness problems with your action. | |
| Jan 31, 2022 at 18:22 | comment | added | Nate | Ahh yea I realized this ordering issue when I was at lunch just now and was going to comment but you beat me to it. The equivalence relation formulation I mentioned instead gives you the coefficients for expanding it in terms of permutation polynomials $j! \binom{x}{j}$. | |
| S Jan 31, 2022 at 17:56 | history | answered | Sam Hopkins | CC BY-SA 4.0 | |
| S Jan 31, 2022 at 17:56 | history | made wiki | Post Made Community Wiki by Sam Hopkins |