Timeline for covering designs of the form $(v,k,2)$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 4, 2015 at 17:40 | vote | accept | Gorka | ||
| Jan 4, 2015 at 6:46 | comment | added | Włodzimierz Holsztyński | @YuichiroFujiwara -- thank you for the links. And I let $\ \frac{\binom{\nu}2}{\binom 32}=\frac{\nu\cdot (\nu-1)}{3\cdot 2}\ $ to have somehow just $\ 3\ $ in the denominator--ooops! Sorry. | |
| Jan 4, 2015 at 6:36 | history | edited | Yuichiro Fujiwara | CC BY-SA 3.0 |
Fixed typos including those pointed out in the comment section. Removed the "group theory" tag.
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| Jan 4, 2015 at 6:31 | comment | added | Yuichiro Fujiwara | @WłodzimierzHolsztyński You can find basic facts in the paper I linked to in my post (or those given by Thomas Kalinowski as well, I think). Handbook of Combinatorial Designs is a good reference book for this sort of basic knowledge; coverings are treated in Section 11 of Chapter IV in the 2nd edition. As for the typos, yes, they are not correct, although the number of $3$-subsets in this case is not $\frac{v(v-1)}{3}$ but $\frac{\binom{v}{2}}{\binom{3}{2}} = \frac{v(v-1)}{6}$. I'll edit OP's post. | |
| Jan 4, 2015 at 1:43 | comment | added | Włodzimierz Holsztyński | Your $\ \frac{n(n-1)}2\ $ must be a typo(?). A simple calculation shows that the number of 3-subset of a $\ (\nu\ 3\ 2)\ $ perfect system must be $\ \frac{\nu\cdot(\nu-1)}3\ $ (it's $\ 3,\ $ not $\ 2,\ $ in the denominator). Also then $\ \nu\equiv 1\ or\ 3\mod 6\ $ (rather than $\ 0\ or\ 3).\ $ Thus I feel that it would be nice and useful for non-specialists like me to have a short list of basic results in a separate Answer. | |
| Jan 3, 2015 at 23:39 | answer | added | Yuichiro Fujiwara | timeline score: 8 | |
| Jan 3, 2015 at 22:28 | comment | added | Włodzimierz Holsztyński | I would call the covering designs $\ (v\ k\ 2)\ $-- sloppy planes. | |
| Jan 3, 2015 at 21:18 | answer | added | Thomas Kalinowski | timeline score: 10 | |
| Jan 3, 2015 at 17:27 | history | asked | Gorka | CC BY-SA 3.0 |