Timeline for Lower bound and limit of a sum with binomial coefficients
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 5, 2022 at 19:05 | answer | added | Jorge Zuniga | timeline score: 3 | |
| Apr 2, 2022 at 4:18 | comment | added | macat | @Jorge Zuniga, 1) I can not write $S_k$ as a single sum whose terms are of the form $a{b\choose c}{d\choose e}$. 2) In my first comment, I was reporting the result given by Maple's Zeilberger function applied to $S_k$ defined as above. | |
| Apr 2, 2022 at 2:00 | comment | added | Jorge Zuniga | Two questions. First, do you have a consolidated numerator summand for $S_k$ of type $a{b\choose c}{d\choose e}$?. Second, how did you get polynomials in k of degree 10?. I think they could be higher. | |
| Apr 1, 2022 at 7:04 | history | edited | macat | CC BY-SA 4.0 |
edited title
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| Mar 31, 2022 at 20:35 | comment | added | macat | Based on an answer to the linked question, one can try to construct a recursion for $S_k$. Using Zeilberger's algorithm, one gets that $p_4S_{k+4}+p_3S_{k+3}+p_2S_{k+2}+p_1S_{k+1}+p_0S_{k}=0$, where the $p_i$'s are polynomials in $k$ with degree 10. This expression seems way too complicated to work with and to show the desired bound for all $k$ without checking the statement for many small $k$'s with a computer. | |
| Mar 31, 2022 at 20:31 | history | asked | macat | CC BY-SA 4.0 |