Timeline for Expanding a combinatorial argument involving permutation coefficients
Current License: CC BY-SA 3.0
9 events
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| Sep 11, 2017 at 14:57 | history | edited | js21 | CC BY-SA 3.0 |
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| Sep 11, 2017 at 14:55 | comment | added | js21 | One needs to count pairs of integers $(p,q)$ with $p$ prime s.t. $q < n k^{-1} + 1$ and $n < pq \leq n+k$. Then for each $q$, we have to bound the number of primes between $nq^{-1}$ and $n q^{-1} + k q^{-1}$. B-T inequality seems to be the natural tool here. | |
| Sep 11, 2017 at 14:51 | comment | added | Gerhard Paseman | Thanks for the edit; I will study it carefully. Does one need Brun-Titchmarsh to carry this through? (I am hoping for more combinatorics and less analytics for a fill in.) Also, >k and >k, or do you really mean >k and >R in your defn of omega_>k? Gerhard "We All Have Our Preferences" Paseman, 2017.09.11. | |
| Sep 11, 2017 at 14:40 | comment | added | js21 | Oh, you are absolutely right! I was confused by the inequalities in the paper; they seem to go the wrong way now. I just added to my answer a proof of the theorem obtained by reversing inequalities... | |
| Sep 11, 2017 at 14:37 | history | edited | js21 | CC BY-SA 3.0 |
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| Sep 11, 2017 at 11:11 | comment | added | Gerhard Paseman | I mean that you are showing W(m,t) has at least t distinct prime factors, which I believe is true for small t, but the result says for large t that W(n,t) (maybe even W(m,t)) has fewer than t distinct prime factors. Or have I gotten things turned around? Gerhard "Maybe Flatten One Extra Hump?" Paseman, 2017.09.11. | |
| Sep 11, 2017 at 8:07 | comment | added | js21 | What do you mean by "fewer prime factors than large $t$" ? | |
| Sep 8, 2017 at 14:24 | comment | added | Gerhard Paseman | Yes, but the theorem says there is n with W(n,t) having fewer prime factors (than large t). Does this argument find such an n? (Even though it is challenging, I believe I can show the existence of $m$ claimed in the proof.) Gerhard "One Fewer Hump Is Needed" Paseman, 2017.09.07. | |
| Sep 8, 2017 at 10:54 | history | answered | js21 | CC BY-SA 3.0 |