Timeline for Residual design (BIBD) with repeated blocks
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 18, 2012 at 12:23 | vote | accept | Mate | ||
| Mar 18, 2012 at 9:41 | answer | added | Vedran Krcadinac | timeline score: 2 | |
| Mar 13, 2012 at 1:32 | comment | added | Noam D. Elkies | Sorry, indeed it seemed to me that you were asking whether any design that already has repeated blocks must have constant multiplicity. For your actual intended question I might have to think some more... | |
| Mar 12, 2012 at 7:33 | history | edited | Mate | CC BY-SA 3.0 |
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| Mar 12, 2012 at 7:28 | comment | added | Mate | @Noam: I don't see how this answers my question :( I gave clarification above. | |
| Mar 12, 2012 at 7:28 | history | edited | Mate | CC BY-SA 3.0 |
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| Mar 12, 2012 at 7:17 | history | edited | Mate | CC BY-SA 3.0 |
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| Mar 12, 2012 at 0:46 | comment | added | Noam D. Elkies | Simple counterexample: $(v,k,\lambda) = (5,1,2)$, $$ {\cal B} = \lbrace \lbrace1,2\rbrace, \lbrace2,3\rbrace, \lbrace3,1\rbrace, \lbrace4,5\rbrace, \lbrace4,5\rbrace \rbrace. $$ | |
| Mar 12, 2012 at 0:32 | comment | added | Noam D. Elkies | There are many counterexamples. As Cameron and van Lint explain in the beginning of their text Designs, Graphs, Codes and Their Links, if $\lambda < k < v-\lambda$ then a $(v,k,\lambda)$ design with repeated blocks is tantamount to a positive solution of a linear system with more variables than equations, and thus always exists, unlike BIBD's without repeats for which $v,k,\lambda$ must satisfy many constraints. | |
| Mar 12, 2012 at 0:14 | history | edited | Mate | CC BY-SA 3.0 |
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| Mar 12, 2012 at 0:08 | history | asked | Mate | CC BY-SA 3.0 |