Timeline for A conjecture on consistent monotone sequences of polynomials in Bernstein form
Current License: CC BY-SA 4.0
36 events
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| Apr 28, 2023 at 13:21 | history | edited | Peter O. | CC BY-SA 4.0 |
condense the question since I believe I have worked around it in the Bernoulli factory case
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| Sep 6, 2022 at 16:39 | history | edited | Peter O. | CC BY-SA 4.0 |
Add equivalent statement
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| Sep 6, 2022 at 16:34 | history | edited | Peter O. | CC BY-SA 4.0 |
Add equivalent statement
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| S Aug 29, 2022 at 1:06 | history | bounty ended | CommunityBot | ||
| S Aug 29, 2022 at 1:06 | history | notice removed | CommunityBot | ||
| Aug 27, 2022 at 0:17 | history | edited | Peter O. | CC BY-SA 4.0 |
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| Aug 23, 2022 at 6:21 | comment | added | Gerry Myerson | Now up to version 19 of this question. | |
| Aug 22, 2022 at 23:41 | history | edited | Peter O. | CC BY-SA 4.0 |
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| Aug 22, 2022 at 23:27 | comment | added | Peter O. | @PietroMajer: Rewrite $r_n$ and $s_n$ (e.g., from the power basis) to the Bernstein form of degree exactly $n+1$ (see the section "Background"), and then take their coefficients in the Bernstein form. These coefficients (labeled $a_k$ in the section "Background") are the Bernstein coefficients (of degree $n+1$) of $r_n$ and $s_n$. | |
| Aug 22, 2022 at 21:44 | history | edited | Peter O. | CC BY-SA 4.0 |
clarification on hypergeometric variable
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| Aug 21, 2022 at 19:41 | history | edited | Peter O. | CC BY-SA 4.0 |
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| Aug 21, 2022 at 17:14 | history | edited | Peter O. | CC BY-SA 4.0 |
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| Aug 21, 2022 at 15:28 | comment | added | Pietro Majer | Thank you. But then would you clarify which are the Bernstein coefficients of the above $r_n$ and $s_n$ exactly? | |
| Aug 21, 2022 at 11:58 | history | edited | Peter O. | CC BY-SA 4.0 |
Clarification
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| Aug 21, 2022 at 11:36 | comment | added | Peter O. | @PietroMajer: $r_n$ and $s_n$ -- not their Bernstein polynomials $B_m r_n$ and $B_m s_n$, which are different in general -- must be polynomials and must have non-negative Bernstein coefficients once they are rewritten to polynomials in Bernstein form of degree exactly $n+1$. | |
| Aug 21, 2022 at 10:05 | comment | added | Pietro Majer | In point 3., $r_n:=g_{n+1}-g_n$ and $s_n:=h_n-h_{n+1}$ are required to be polynomials of degree exactly equal to or not larger than $n+1$? And the coefficients of their Bernstein polynomial $B_mr_n$ and $B_ms_n$ of what order $m$ are required to be non-negative? | |
| Aug 21, 2022 at 6:21 | history | edited | Peter O. | CC BY-SA 4.0 |
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| Aug 21, 2022 at 5:12 | history | edited | Peter O. | CC BY-SA 4.0 |
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| Aug 21, 2022 at 4:59 | history | rollback | Peter O. |
Rollback to Revision 10
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| Aug 21, 2022 at 4:52 | history | rollback | Peter O. |
Rollback to Revision 9
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| Aug 21, 2022 at 4:46 | history | edited | Peter O. | CC BY-SA 4.0 |
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| Aug 20, 2022 at 23:56 | history | edited | Peter O. | CC BY-SA 4.0 |
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| S Aug 20, 2022 at 23:56 | history | bounty started | Peter O. | ||
| S Aug 20, 2022 at 23:56 | history | notice added | Peter O. | Canonical answer required | |
| Aug 17, 2022 at 23:12 | history | edited | Peter O. | CC BY-SA 4.0 |
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| Aug 16, 2022 at 21:26 | history | edited | Peter O. | CC BY-SA 4.0 |
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| Aug 16, 2022 at 21:24 | history | undeleted | Peter O. | ||
| Aug 16, 2022 at 21:01 | history | deleted | Peter O. | via Vote | |
| Aug 16, 2022 at 21:01 | history | undeleted | Peter O. | ||
| Aug 4, 2022 at 8:22 | history | deleted | Peter O. | via Vote | |
| Aug 2, 2022 at 19:16 | history | edited | Peter O. | CC BY-SA 4.0 |
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| Aug 2, 2022 at 19:08 | history | edited | Peter O. | CC BY-SA 4.0 |
Another conjecture
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| Aug 2, 2022 at 5:44 | history | edited | Peter O. |
Add conjectures tag
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| Jul 31, 2022 at 13:38 | history | edited | Peter O. | CC BY-SA 4.0 |
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| Jul 31, 2022 at 11:59 | history | edited | Peter O. | CC BY-SA 4.0 |
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| Jul 31, 2022 at 11:19 | history | asked | Peter O. | CC BY-SA 4.0 |