Timeline for What are $(m,n)$-pseudoplanes?
Current License: CC BY-SA 4.0
9 events
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| Oct 4, 2018 at 13:56 | comment | added | Nick Gill | I guess you know about symmetric balanced incomplete block designs? They are not defined via your two properties but I think they satisfy them... People usually study them for your parameter $m$ being equal to $2$, although I don't see why this is necessary. I don't have time now to think this through properly so will leave this as a comment... | |
| Oct 4, 2018 at 13:36 | history | edited | Alex Kruckman | CC BY-SA 4.0 |
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| Oct 1, 2018 at 17:12 | history | edited | Alex Kruckman | CC BY-SA 4.0 |
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| Jun 14, 2018 at 11:49 | comment | added | Alex Kruckman | @AaronMeyerowitz Yes, thanks. Note that I'm not assuming finiteness - it's easy to build infinite examples by starting with a $K_{m,n}$-free configuration and adjoining points and lines "freely" to satisfy the axioms. | |
| Jun 14, 2018 at 11:46 | history | edited | Alex Kruckman | CC BY-SA 4.0 |
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| Jun 14, 2018 at 8:21 | comment | added | Aaron Meyerowitz | I'm sure that you mean: For every n distinct lines, there are exactly (m−1) distinct points which are incident to all of them. Do you know non-trivial examples? I can see that the triples from a $4$ point set are a $(3,2)$ but that seems like the only one. | |
| Jun 13, 2018 at 19:57 | comment | added | Gerhard Paseman | More an idea than a reference. This looks to me like a set covering or lottery system (how many tickets to guarantee one of them has two of the five numbers). Relax a condition, find the common structure, then see if someone has specialized it to your case. Gerhard "Good Luck In Your Search" Paseman, 2018.06.13. | |
| Jun 13, 2018 at 19:31 | history | edited | Alex Kruckman | CC BY-SA 4.0 |
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| Jun 13, 2018 at 19:26 | history | asked | Alex Kruckman | CC BY-SA 4.0 |