Timeline for Demonstrate another way to implement the Inclusion–exclusion principle?
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 6 at 18:01 | comment | added | MikeTeX | Very nice and instructive answer. | |
| Mar 6 at 17:59 | comment | added | MikeTeX | N(j) = $\sum_{n\geq j} a_n {n \choose j}$, where $a_n$ is the number of elements that are exactly in $n$ of the $S(i)$. Then the cancelation lemma implies that $\sum_{j \geq k} (-1)^{j-k} {j \choose k} N(j) = a_k$. | |
| Mar 6 at 17:59 | comment | added | MikeTeX | OK. Note: I would write your proof of (6) as follows: | |
| Mar 6 at 17:52 | comment | added | robjohn♦ | For $0\le j\lt k$, $\binom{j}{k}=0$, so starting at $0$ or $k$ gives the same result. My personal preference is to start at $0$ as that often proves easier in cases where the order of summation needs to be changed. | |
| Mar 6 at 17:37 | comment | added | MikeTeX | Typo: I think in (6), the index j should start from k. | |
| Aug 30, 2021 at 3:10 | history | bounty ended | linear_combinatori_probabi | ||
| Sep 3, 2020 at 3:51 | history | bounty ended | linear_combinatori_probabi | ||
| Oct 29, 2019 at 7:56 | history | edited | robjohn♦ | CC BY-SA 4.0 |
improve the explanation of $\binom{-1}{n}$
|
| Oct 28, 2019 at 22:42 | history | edited | robjohn♦ | CC BY-SA 4.0 |
add Corollary 2
|
| Oct 16, 2019 at 2:34 | history | edited | robjohn♦ | CC BY-SA 4.0 |
color the theorem and corollary the same as the lemma
|
| Oct 15, 2019 at 23:00 | history | edited | robjohn♦ | CC BY-SA 4.0 |
fix a minor point
|
| Oct 15, 2019 at 19:43 | history | edited | darij grinberg | CC BY-SA 4.0 |
added 2 characters in body
|
| Oct 15, 2019 at 19:04 | history | edited | darij grinberg | CC BY-SA 4.0 |
the factorial formula requires n >= k
|
| Oct 15, 2019 at 18:59 | history | edited | darij grinberg | CC BY-SA 4.0 |
the factorial formula requires n >= k
|
| Oct 5, 2019 at 13:24 | history | edited | robjohn♦ | CC BY-SA 4.0 |
improve the subscripts for the underbraces
|
| Jul 12, 2017 at 15:21 | history | edited | robjohn♦ | CC BY-SA 3.0 |
Add $(5)$
|
| Sep 28, 2016 at 13:28 | history | edited | robjohn♦ | CC BY-SA 3.0 |
improve underbrace
|
| Sep 11, 2013 at 23:08 | history | edited | robjohn♦ | CC BY-SA 3.0 |
fix typo
|
| Jul 6, 2013 at 14:43 | history | edited | robjohn♦ | CC BY-SA 3.0 |
add a corollary
|
| Jun 11, 2013 at 0:09 | history | edited | robjohn♦ | CC BY-SA 3.0 |
renumber
|
| Jun 11, 2013 at 0:03 | history | edited | robjohn♦ | CC BY-SA 3.0 |
add the simplest proof of the cancellation lemma
|
| Apr 15, 2013 at 21:48 | history | edited | robjohn♦ | CC BY-SA 3.0 |
add a second proof
|
| Apr 15, 2013 at 16:27 | history | answered | robjohn♦ | CC BY-SA 3.0 |