Timeline for Counting monomials in product polynomials: Part II
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jan 23, 2021 at 20:18 | vote | accept | T. Amdeberhan | ||
| Jan 11, 2021 at 17:15 | comment | added | T. Amdeberhan | @FedorPetrov: that is interesting. | |
| Jan 11, 2021 at 17:15 | history | edited | T. Amdeberhan | CC BY-SA 4.0 |
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| Jan 11, 2021 at 0:36 | comment | added | Fedor Petrov | by the way, this is Chebyshev-related polynomial, its roots are $4\cos^2 \pi k/(e+2)$, $0<k<e+2$, so the growth of $a_{n,e}$ for large $n$ is $C_e\times (2\cos \pi/(e+2))^{2n}$. | |
| Jan 10, 2021 at 15:37 | history | edited | T. Amdeberhan | CC BY-SA 4.0 |
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| Jan 9, 2021 at 23:41 | answer | added | Fedor Petrov | timeline score: 5 | |
| Jan 9, 2021 at 21:54 | comment | added | T. Amdeberhan | @RichardStanley: I had my share of such too. :-) | |
| Jan 9, 2021 at 21:18 | comment | added | Richard Stanley | Yow! You are right. I had an error in my code. Good conjecture! | |
| Jan 9, 2021 at 21:06 | comment | added | T. Amdeberhan | @RichardStanley: my count shows 121 not 119. I'm not sure if I made a mistake. The counts $a_{n,4}$ according to Maple are: 1, 4, 13, 40, 121, 364, 1093, etc | |
| Jan 9, 2021 at 20:30 | comment | added | Richard Stanley | Let $e=4$. According to my computations, the number of monomials in $P_{5,4}(x)$ is 119, while the coefficient of $y^5$ in $y/(1-4y+3y^2)$ is 121. | |
| Jan 9, 2021 at 17:36 | history | edited | Fedor Petrov | CC BY-SA 4.0 |
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| Jan 9, 2021 at 17:13 | history | edited | T. Amdeberhan | CC BY-SA 4.0 |
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| Jan 9, 2021 at 16:59 | history | asked | T. Amdeberhan | CC BY-SA 4.0 |