Timeline for Blocking set in a projective plane.
Current License: CC BY-SA 2.5
14 events
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| Aug 15, 2010 at 19:44 | history | edited | Andreas Thom |
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| Aug 14, 2010 at 22:55 | comment | added | damiano | If you do not mind, I would edit the question to make it self-contained as follows. Let $\mathbb{P}$ be the set of points of the projective plane over a finite field with q elements. A blocking set in $\mathbb{P}$ is a subset $S \subset \mathbb{P}$ such that $S$ contains no line and every line in $\mathbb{P}$ has at least one point in common with $S$. Let $A$ be a subset of $\mathbb{P}$ and suppose that for every blocking set $S$ we have $A \cap S \neq \emptyset$. Question: is it true that $|A| \geq q+1$, and that if equality holds, then $A$ is a line? | |
| Aug 14, 2010 at 19:29 | vote | accept | jeff | ||
| Aug 14, 2010 at 16:00 | answer | added | damiano | timeline score: 2 | |
| Aug 14, 2010 at 14:50 | comment | added | jeff | OK, i've edited my original post to the words of damiano as this is exactly what i mean :) Sorry for the trouble. | |
| Aug 14, 2010 at 14:49 | history | edited | jeff | CC BY-SA 2.5 |
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| Aug 14, 2010 at 14:30 | comment | added | Gerry Myerson | @jeff, blocking set is the right term, what has confused everyone is that you defined a blocking set to be a set that doesn't contain a line, when what you meant is what you said in your last comment. I suggest you withdraw your question and re-enter it the way it should be. | |
| Aug 14, 2010 at 14:28 | comment | added | damiano | I see: a blocking set is a subset $S$ of the projective plane with the property that every line has at least one point in common with $S$. You require such a blocking set to not contain any line, and then you want to ask the question about $A$, ranging over all non-trivial blocking sets. Is this a correct interpretation? The wording in your question is quite difficult to parse, for someone not familiar with the notion of a blocking set. | |
| Aug 14, 2010 at 14:25 | comment | added | jeff | So in my question: S = ANY of these sets such that there is no line in them | |
| Aug 14, 2010 at 14:23 | comment | added | jeff | Then i suppose i'm using the wrong term for blocking set. What i mean is: Set of points such that each line from the projective plane consists at least one of these points. | |
| Aug 14, 2010 at 14:13 | comment | added | jeff | I've mentioned that for each blocking set S that doesn't contain a line, and according to Bruen, |S| >= q + sqrt(q) + 1 so how what singeltons have to do here? So i want A to intersect every blocking set S that doesn't contain a line. | |
| Aug 14, 2010 at 13:48 | comment | added | jeff | I'm sorry, the definition is for ANY blocking set S, therefore you cannot take a concrete one. | |
| Aug 14, 2010 at 13:30 | comment | added | jeff | p contains a line so it cannot be a blocking set. | |
| Aug 14, 2010 at 10:33 | history | asked | jeff | CC BY-SA 2.5 |