Talk:Inclusion–exclusion principle

message: I added the parenthesis with the synonym 'sieve principle'; and didn't notice until after saving that I was auto-logged out.  Just so that you know whom to blame...JoergenB 14:25, 27 September 2006 (UTC)
replies: text: I've actually never heard it referred to as the sieve principle, but I am not a combinatorist. I usually associate "sieve" with the sieve of eratosthenes or other number theoretic sieves. Of course these are applications of the inclusion-exclusion principle.--CSTAR 15:31, 27 September 2006 (UTC)
replies: text:  I never heard of it being called the "sieve principle" either. I reverted for now, perhaps the contributor who added that can come up with some references. Oleg Alexandrov (talk) 01:39, 28 September 2006 (UTC)
replies: text:  Combinatorics folks call it the sieve formula quite often.  The first example that came up in a search was K. Dohmen, Some remarks on the sieve formula, the Tutte polynomial and Crapo's beta invariant, Aequationes Mathematicae, 	Volume 60, Numbers 1-2 / August, 2000.  Searching for "sieve formula" at scholar.google.com finds other examples too (but not all hits are to inclusion-exclusion). McKay 04:01, 4 October 2006 (UTC)

text: Another example is in Stanley's Enumerative Combinatorics, where it is called a sieve method, although it seems to be considered only one of many. Cheeser1 23:46, 1 April 2007 (UTC)
replies: text: Combinatorics people quite often don't call it a sieve method.  I find the connection rather strained.  Opinions differ as you can see.  I edited the language from "is" to "can be viewed as".  Zaslav (talk) 23:15, 12 May 2022 (UTC)
thread_title:  Sieve principle 

message: The diagram currently for n=4 appears to depict a special case where - labelling the 4 sets going clockwise around the diagram say, A,B,C,D - the number of elements in the intersection of A & C which are not in B or D is zero, and the number of elements in the intersection of B & D not in A or C is also zero.  This could lead students to derive alternative incorrect formulae, such as:  
:\begin{align}|A\cup B\cup C\cup D|&=|A|+|B|+|C|+|D|\\
&\qquad-|A\cap B|-|B\cap C|-|C\cap D|-|D\cap A|+|A\cap B\cap C\cap D|
\end{align}
I think the special case diagram is likely to lead to faulty reasoning, and would be better either removed or replaced with something catering for the general case. Stumps (talk) 03:35, 27 June 2008 (UTC)
replies: text: Maybe using something like? Anyone a better artist? Stumps (talk) 05:18, 27 June 2008 (UTC)

text: My brain just exploded. I was always told that no "Venn Diagram" could be drawn for n > 3, and yet your picture seems to accomplish it. Perhaps my over-zealous school teachers meant it couldn't be done using only circles, which is indeed true. Austinmohr (talk) 04:47, 14 March 2010 (UTC)
thread_title:  Diagram for ''n''=4 

message: You might want to take a look at the approach given in Inclusion-Exclusion Principle in ProofWiki (a fast-growing baby sibling of this one).
The emphasis here is on the general additive function, which automatically takes on board the counting function and the probability measure (in fact, any measure you care to consider).
The proof itself is inductive and purely algebraic, in that it does not use anything more complicated than an (admittedly) intuitive appeal to "all subsets of order s out of \left\{{1, 2, \ldots, r}\right\}" in order to get the correct sum of the contributions of the intersections of s subsets of r.
IMO it's easier to follow (well I would think that, I wrote it). --WestwoodMatt (talk) 07:46, 3 March 2010 (UTC)
thread_title:  How about a proof by induction? 

message: I am almost finished with my refactoring of this article. I've expanded the lead to make it readable, clarified the statement of the principle, talked about special cases and generalizations and vastly expanded the list of applications. I am now moving on to improve some of the mathematical writing. Before tackling the proofs (which I have moved to the end of the article, where they belong) I want to redo the section on Möbius inversion (titled "Other forms" - that will be changed!). My usual modus operandi is to leave as much of what previous editors have contributed alone and build up the section with small corrections and changes. I especially don't like to touch referenced material that I don't have access to. In this section however, I feel that I need to make some major changes. The statement of the result is not accurate, the presentation leaves much to be desired and the emphasis seems a bit skewed. This may not be the fault of the editor, but rather the reference that was used. I am planning on replacing the reference with something a bit more mainstream as I redo the section and I am afraid that not much of what is currently there will survive. Any comments before I do this? Bill Cherowitzo  (talk) 03:25, 1 April 2013 (UTC)
thread_title:  Möbius inversion  

message: The "Alternative proof" at the end is essentially exactly the same as the "First possibility" under "Proof".  I could redo this, but might be better if someone familiar with the page did.
Thanks!
Natkuhn (talk) 02:56, 22 December 2014 (UTC)
replies: text: Sorry, I meant to do this last year but it kinda fell off my radar. I'll put the algebraic proof back in a few days after I polish it up a bit. Bill Cherowitzo  (talk) 19:38, 22 December 2014 (UTC)
thread_title:  Can the proofs be cleaned up? 

message: The text (in the introductory part) says "This concept is attributed to Abraham de Moivre (1718);[1] but it first appears in a paper of Daniel da Silva (1854),[2] and later in a paper by J. J. Sylvester (1883).[3]" 
But 1718 is long before 1854, so what does this text mean? Did de Moivre not actually write about the principle but people cite him anyway for some reason? Or is it just a mistake with the dates? It's hard to tell because de Moivre (1718) isn't actually listed in the references. Nathaniel Virgo (talk) 09:17, 2 July 2018 (UTC)
replies: text: The statement in Roberts and Tesman is that de Moivre wrote the principle in another form. They then reference this to his book, The Doctrine of Chances, privately printed in London in 1718. The form of the principle as stated in this article can be traced back to da Silva and Sylvester. --Bill Cherowitzo  (talk) 17:23, 2 July 2018 (UTC)
thread_title:  Can the text about the origin of the concept be clarified? 

message: To count the number of elements in exactly k sets, the coefficient for the intersection of m sets is (-1)^{m+k} {m \choose k}
In the normal case this results in coefficients 1, -1, 1, -1, ... 
For elements in exactly 1 set this is 0, 1, -2, 3, -4, ...
For elements in exactly 2 sets this is 0, 0, 1, -3, 6, -10, ...
I believe this result is in textbooks but it's strangely hard to find it on the internet. I don't have a proof though so this result and the proof should be added to the article. Wqwt (talk) 06:47, 20 August 2018 (UTC)
replies: text: I just found it here with reference https://math.stackexchange.com/questions/1808129/generalised-inclusion-exclusion-principle Wqwt (talk)  —Preceding undated comment added 07:07, 20 August 2018 (UTC)
thread_title:  Generalization to elements in exactly k sets 

message: By Samuel Monnier - Own work (low res file), CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=8481291  — Preceding unsigned comment added by Noosphericus (talk • contribs) 19:55, 28 December 2018 (UTC)
thread_title:  By Samuel Monnier - Own work (low res file), CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=8481291 

message: "where the last sum runs over all subsets I of the indices 1, ..., n which contain exactly k elements, and .."
no: I runs over all n-uples.. etc. Please amend--Federicolo (talk) 13:37, 1 January 2021 (UTC)
thread_title:  mistake : confusion between n-uple and set