Timeline for Families of subsets with pairwise symmetric differences of cardinality at most $k$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 29, 2015 at 11:50 | comment | added | Francis Raj S | We also hope that this will happen. Is there any way to prove your statement. | |
| Sep 29, 2015 at 11:35 | comment | added | usul | Assuming that's right, since $N(\mathcal{F})$ is the intersection of the Hamming balls of size $k$ around each $A \in \mathcal{F}$ minus $\mathcal{F}$, surely $\mathcal{F}$ must be as "clumped" as possible? (i.e. a Hamming ball when $l$ is the correct size). For instance, if we decrease the distance of some $A \in \mathcal{F}$ to every other $B \in \mathcal{F}$, then we only increase $|N(\mathcal{F})|$. | |
| Sep 29, 2015 at 11:33 | comment | added | usul | Just want to clarify two things: (1) $l$ is given and fixed and we want to find the optimal $\mathcal{F}$ of that size, right? (2) The definition of $N(\mathcal{F})$ is correctly written "for all $A \in \mathcal{F}$"? (It shouldn't be "for some $A \in \mathcal{F}$"?) | |
| Sep 29, 2015 at 10:16 | comment | added | Fedor Petrov | There is Harper's isoperimetric bound in Hamming cube (estimate size of the neighborhood via size of the set), but I do not know about isodiametric problem (maximal size of the set with given diameter). | |
| Sep 29, 2015 at 9:28 | history | edited | domotorp | CC BY-SA 3.0 |
changed mathbb to mathcal
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| Sep 28, 2015 at 13:59 | history | edited | j.c. | CC BY-SA 3.0 |
improve title, add quantifier
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| Sep 28, 2015 at 13:11 | review | First posts | |||
| Sep 28, 2015 at 13:47 | |||||
| Sep 28, 2015 at 13:06 | history | asked | Francis Raj S | CC BY-SA 3.0 |