Talk:Incidence algebra

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated Start-class, Mid-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
Start Class
Mid Importance
 Field:  Algebra

Questions[edit]

I take it the zeta function is always invertible? (I figured that one out.) Is there a characterization of the invertible elements in the algebra? AxelBoldt 23:36 Jan 8, 2003 (UTC)

Mike, non-logged in users cannot mark edits as "minor" anymore, because some have used that to hide vandalism. Maybe it would be good if you logged in anyway, because then people could leave you messages on your user page. AxelBoldt 04:36 Jan 9, 2003 (UTC)

What is exactly the connection with classical Euler characteristic ? Is the classical Euler ch. equal to the incidence Euler ch. of the poset of faces of the polyhedron ? It would be nice to put that information both in this article and in Euler characteristic. --FvdP 18:47 Jan 9, 2003 (UTC)

Good question. I find I can't answer it as quickly and efficiently as I would have hoped; stay tuned ..... -- Mike Hardy

I added a sentence about this (and took out the sentence that μ(0,1) is always an integer, as the Mobius function is integral by definition). Dotdotdotatsignapostrophe (talk) 22:54, 14 October 2013 (UTC)

Is it easy to see that the Mobius function defined as in the article is both an inverse on the right and on the left to zeta, or is it necessary to go along the lines of "by two similar but different constructions, zeta is invertible on the left and on the right, hence said inverse is the same on both sides"?SamBaum (talk) 21:45, 1 November 2013 (UTC)

Possible move[edit]

Having looked at the several articles dealing with aspects of Moebius inversion on posets, I have come to realize that this topic needs some reorganization. This is a beautiful, unifying concept in combinatorics and one does not see that from these articles unless you already know what to look for. In this article, the topic in its general form is most clearly laid out, but it is buried under an article title which does not hint at this content. I think that this article should be called Moebius inversion (combinatorics) and it should contain a section on the most general order/algebraic setting in which such inversions are defined, i.e., Incidence algebras. To support this move I'd point out that most of the links to this page are links to Moebius inversion and in the text treatments of Moebius inversion, the term incidence algebra is rarely used. There may be other ways to deal with this issue and I'd like to hear some suggestions. Bill Cherowitzo (talk) 20:48, 29 December 2014 (UTC)

Confusion about the definition[edit]

I've been learning about incidence algebras by reading different articles on the internet, and the definition given here strikes me as incomplete. Currently it sounds like you could just pick any functions f[a,b], regardless of how a and b relate. Elsewhere I've read that if a !≤ b, then f(a,b) = 0.[1] It's also unclear how different choices of f(a,b) relate to each other. What if I picked f[a,b] = 4 and some other person picked f[a,b] = -30. Would we be dealing with "different incidence algebras"? "Different bases"? I'm just scratching my head in wonder for now :) Macaw scopes (talk) 22:21, 29 January 2016 (UTC)