Timeline for Sets of natural numbers such that sums of a bounded number of its elements form a semigroup
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Apr 26, 2016 at 1:33 | history | bounty ended | CommunityBot | ||
| S Apr 26, 2016 at 1:33 | history | notice removed | CommunityBot | ||
| S Apr 18, 2016 at 0:06 | history | bounty started | Michał Masny | ||
| S Apr 18, 2016 at 0:06 | history | notice added | Michał Masny | Draw attention | |
| Apr 23, 2015 at 0:40 | vote | accept | Michał Masny | ||
| Apr 17, 2015 at 19:28 | comment | added | Michał Masny | @Mirko I think it's simpler to think about the case of sets containing zero only. | |
| Apr 16, 2015 at 11:29 | answer | added | J.-E. Pin | timeline score: 6 | |
| Apr 16, 2015 at 7:31 | comment | added | Mirko | my comment above assumes that $\langle A\rangle=\mathbb N$. I may not understand what is "the semigroup generated by $A$". If $A$ contains all positive multiples of $3$, and all multiples of $5$ starting with $15$, is then $\langle A\rangle = \{3,6,9,12,15,18,20,21,23,24,25,...\}$ thus containing all positive integers beyond $23$ (yet not containing $1,2,4,5,7,8,10,11,13,14,16,17,19,22$)? Does it have to contain $0$? I guess $A$ itself (and hence $\langle A\rangle$ too) should contain $0$ (since you require it explicitly). | |
| Apr 16, 2015 at 6:19 | comment | added | Mirko | Fix $n$ and try to see which $A$ work for this $n$. For example, for $n=3$, the set $A=\{0,1,4,7,10,...,3k+1,...\}$ easily works, but so also does the set $A=\{0,1,3,7,12,18,..\}$ even though for the latter the gaps between consecutive numbers become bigger and bigger (and even though I don't know what is the common term). We could have used $23$ instead of $18$, but making bigger gaps early may necessitate making smaller gaps later. I am pretty sure that for $n=3$ the set of triangular numbers $A=\{0,1,3,6,10,15,21,..,\dfrac{n(n+1)}2,..\}$ works(?) providing example where the gaps get larger. | |
| Apr 15, 2015 at 21:16 | history | asked | Michał Masny | CC BY-SA 3.0 |