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An incidence structure is not a concept belonging to combinatorial mathematics unless the sets involved are finite (from this point of view, graphs and hypergraphs with an infinite number of vertices are not combinatorial objects either.) The only reference given clearly has a bias toward calling things combinatorial. Incidence structures arise in geometry, but they are more general than that subject. There is no particular reason to place this concept in any subtopic of mathematics (Combinatorics, Geometry, Design Theory, etc.). We are simply talking about two sets with a symmetric relation between them, a structure that can come up in any discipline (and saying that it "belongs" to Set Theory, just doesn't say anything to most readers). Wcherowi ( talk) 04:46, 1 September 2011 (UTC)
Can someone clear up the distinction between Incidence structure and Incidence geometry? 195.77.88.65 ( talk) 20:46, 15 April 2014 (UTC)
What about to arbitrary dimension? 79.180.20.102 ( talk) 16:29, 8 October 2014 (UTC)
The article now states
This surprises me a bit.
Actually, the author of the sentence seems to take for granted that the only natural way to consider an incidence structure as a graph is by letting the lines in the structure somehow correspond to the edges in the graph. On the other hand, when e.g. there is a reference in Cage (graph theory)#Known cages to some cages as "incidence graphs", this implicitly treats the point set and the line set as the two parts in a bipartite graph, whose edges are given by the incidences. I would have expected a reference to this point of view here (if for no other reason to serve as a more adequate direct reference from the cages article).
Does anybody see a good reason not to rewrite the section, making the bipartite graph the principal example, and demoting the hypergraph interpretation to a secondary one? JoergenB ( talk) 11:54, 25 May 2015 (UTC)
In Incidence structure#Formal definition and terminology I think we are missing some rules.
As it stands at the moment all of the following are possible:
a: two lines sharing the same set of points
b: three points being part of two different lines
c: two points not having a connecting line
and maybe even more "strange" incidence possibilities. (add your own if you like)
If these possibilities are indeed possible I think they should be mentioned and I would like to have a (sub) section "related subjects" that links to structures / geometry / subject have a more limited definition.
Unfortunedly I am not knowledgable enough in this subject to write about it myself, also maybe different authors will have different definitions, but lets work on a wikipedia definition here :) WillemienH ( talk) 19:08, 19 December 2015 (UTC)
I would then suggest to reorder the article, I want to move the examples down because they all just represent a small subset of all possibilities (while other parts like dual structure and representation seems applicable to all incidence structures. WillemienH ( talk) 22:24, 19 December 2015 (UTC)
Incidence complex is currently a red link. Should it be a redirect here as a synonym or subtopic, or is it a distinct object of study in its own right? — Cheers, Steelpillow ( Talk) 08:58, 28 September 2022 (UTC)
This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
An incidence structure is not a concept belonging to combinatorial mathematics unless the sets involved are finite (from this point of view, graphs and hypergraphs with an infinite number of vertices are not combinatorial objects either.) The only reference given clearly has a bias toward calling things combinatorial. Incidence structures arise in geometry, but they are more general than that subject. There is no particular reason to place this concept in any subtopic of mathematics (Combinatorics, Geometry, Design Theory, etc.). We are simply talking about two sets with a symmetric relation between them, a structure that can come up in any discipline (and saying that it "belongs" to Set Theory, just doesn't say anything to most readers). Wcherowi ( talk) 04:46, 1 September 2011 (UTC)
Can someone clear up the distinction between Incidence structure and Incidence geometry? 195.77.88.65 ( talk) 20:46, 15 April 2014 (UTC)
What about to arbitrary dimension? 79.180.20.102 ( talk) 16:29, 8 October 2014 (UTC)
The article now states
This surprises me a bit.
Actually, the author of the sentence seems to take for granted that the only natural way to consider an incidence structure as a graph is by letting the lines in the structure somehow correspond to the edges in the graph. On the other hand, when e.g. there is a reference in Cage (graph theory)#Known cages to some cages as "incidence graphs", this implicitly treats the point set and the line set as the two parts in a bipartite graph, whose edges are given by the incidences. I would have expected a reference to this point of view here (if for no other reason to serve as a more adequate direct reference from the cages article).
Does anybody see a good reason not to rewrite the section, making the bipartite graph the principal example, and demoting the hypergraph interpretation to a secondary one? JoergenB ( talk) 11:54, 25 May 2015 (UTC)
In Incidence structure#Formal definition and terminology I think we are missing some rules.
As it stands at the moment all of the following are possible:
a: two lines sharing the same set of points
b: three points being part of two different lines
c: two points not having a connecting line
and maybe even more "strange" incidence possibilities. (add your own if you like)
If these possibilities are indeed possible I think they should be mentioned and I would like to have a (sub) section "related subjects" that links to structures / geometry / subject have a more limited definition.
Unfortunedly I am not knowledgable enough in this subject to write about it myself, also maybe different authors will have different definitions, but lets work on a wikipedia definition here :) WillemienH ( talk) 19:08, 19 December 2015 (UTC)
I would then suggest to reorder the article, I want to move the examples down because they all just represent a small subset of all possibilities (while other parts like dual structure and representation seems applicable to all incidence structures. WillemienH ( talk) 22:24, 19 December 2015 (UTC)
Incidence complex is currently a red link. Should it be a redirect here as a synonym or subtopic, or is it a distinct object of study in its own right? — Cheers, Steelpillow ( Talk) 08:58, 28 September 2022 (UTC)