Timeline for Can this be interpreted as one Euler characteristic?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 13, 2022 at 7:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 15, 2021 at 7:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| May 18, 2021 at 6:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 18, 2021 at 5:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 20, 2020 at 8:19 | comment | added | Max Alekseyev | It do not see how exactly "rewriting" of the formulae works here, but they can be viewed as an application of the inclusion-exclusion principle applied to the sets $$\{x\in [n]\ :\ p_i\mid x\}.$$ | |
| Sep 20, 2020 at 5:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 10, 2020 at 1:06 | history | edited | Michael Hardy | CC BY-SA 4.0 |
added 20 characters in body
|
| Mar 9, 2020 at 11:24 | comment | added | Wlod AA | $\sum_{k=0}^n(-1)^k\cdot\binom nk = 0\ $ because $(n-1)$-simplex is acyclic. Also, $\ \sum_{k=0}^n (-1)^k\cdot 2^{n-k}\cdot\binom nk = 1\ $ because $n$-cube is acyclic, etc. | |
| Mar 9, 2020 at 10:50 | comment | added | Wlod AA | Euler characteristic is based on the equation between the alternative sums of ranks of two kinds of groups (chains vs homology). Do you have two seemingly unrelated kinds of objects, etc. ? | |
| Mar 9, 2020 at 1:58 | comment | added | Will Sawin | we can write $\omega( \prod_{x\in A} x ) $ as the sum over $p<n$ of $1$ if $p$ divides $x$ for some $x$ in $A$ and $0$ otherwise. Exchanging the order of summation proves your identity. This makes me think, if it's an Euler characteristic, this will just be a space that is a disjoint union over the primes. | |
| Mar 8, 2020 at 20:08 | comment | added | user6671 | @DanielD. thanks for your comment | |
| Mar 8, 2020 at 20:04 | comment | added | Dabed | +1, I had never seen this identity pretty cool it if I understand correctly it gives 0 because it is an inclusion-exclusion formula, I read this question and came back to see if someone answered but it was deleted so is nice too see it back | |
| Mar 8, 2020 at 18:08 | history | undeleted | user6671 | ||
| Mar 8, 2020 at 17:52 | history | deleted | user6671 | via Vote | |
| Mar 8, 2020 at 10:09 | history | asked | user6671 | CC BY-SA 4.0 |