Timeline for a block design question: Does every special 1-design admit a partition which respects enough of the blocks?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 12, 2016 at 19:29 | history | edited | Gerhard Paseman | CC BY-SA 3.0 |
Need more descriptive title
|
| Dec 17, 2013 at 20:05 | answer | added | Gerhard Paseman | timeline score: 3 | |
| Dec 17, 2013 at 10:58 | history | edited | j.s. | CC BY-SA 3.0 |
added 36 characters in body
|
| Dec 17, 2013 at 10:58 | comment | added | j.s. | Douglas Zare, $v$ is a multiple of $3$. | |
| Dec 17, 2013 at 10:54 | comment | added | j.s. | Yuichiro Fujiwara; I correct my question. $k$ for $Q$ is $4$. | |
| Dec 17, 2013 at 10:52 | history | edited | j.s. | CC BY-SA 3.0 |
edited body
|
| Dec 15, 2013 at 23:22 | comment | added | Douglas Zare | If you are looking at $t=1, \lambda=1$ then you just have a partition. A necessary condition to have a disjoint collection of sets of size $3$ covering everything is that the number of points is divisible of $3$. However, you can have a regular hypergraph of degree $4$ so the number of points is not divisible by $3$. For example, $4$ copies of a $4$ element set, or less trivially the complements of lines in the Fano plane which has $7$ vertices. | |
| Dec 15, 2013 at 17:02 | comment | added | Yuichiro Fujiwara | I don't quite follow what you mean by "such that every block of $Q$ is some block of $D$ that one of its elements is removed." Can you rephrase it or explain exactly what you mean by an example? Did you mean $Q$ is a triple system instead of block size $4$? Or is it of order $v-1$ rather than $v$? | |
| Dec 15, 2013 at 15:20 | comment | added | j.s. | Douglas Zare, yes. I am looking at $t=1$. | |
| Dec 14, 2013 at 23:12 | comment | added | Douglas Zare | What do you mean by a $1$-design? Normally block designs parameters are given as $(v,k,\lambda)$ or $t-(v,k,\lambda)$ where $t \ge 2$. Are you really looking at $t=1$, regular hypergraphs? | |
| Dec 14, 2013 at 21:23 | history | edited | j.s. | CC BY-SA 3.0 |
deleted 1 characters in body
|
| Dec 14, 2013 at 20:18 | history | edited | j.s. | CC BY-SA 3.0 |
edited body
|
| Dec 14, 2013 at 19:43 | history | asked | j.s. | CC BY-SA 3.0 |