Timeline for Decomposing a set of integers as a union of well-separated (discrete) intervals
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 2, 2023 at 21:14 | comment | added | Salvo Tringali | @bof Right. It's also the shortest length of a factorization of the set $S$ as a union of (non-empty, discrete) intervals in the commutative monoid obtained by endowing the power set of $\mathbb Z$ with the binary operation $(X,Y) \mapsto X \cup Y$. The "shortest factorization length" is an arithmetic invariant studied in a variety of settings for a wide range of "building blocks" (or "elementary factors") that one may want to use all along the factorization process. So, I find this point of view more natural. | |
| Feb 21, 2023 at 16:29 | history | edited | Salvo Tringali | CC BY-SA 4.0 |
fixed further details and added an obvious upper bound on bim(S)
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| Feb 18, 2023 at 22:03 | comment | added | bof | In other words, $\operatorname{bim}(S)$ is the number of connected components in the graph $G$ with vertex set $V(G)=S$ and edge set $E(G)=\{\{x,y\}\subseteq S:|x-y|=1\}$. Right? | |
| Feb 18, 2023 at 21:56 | history | edited | Salvo Tringali | CC BY-SA 4.0 |
fixed another (and more critical) detail
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| Feb 18, 2023 at 18:25 | history | became hot network question | |||
| Feb 18, 2023 at 17:00 | history | edited | RobPratt |
edited tags
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| Feb 18, 2023 at 11:26 | history | edited | Salvo Tringali | CC BY-SA 4.0 |
added examples
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| Feb 18, 2023 at 10:56 | answer | added | Pedro A. Garcia-Sanchez | timeline score: 3 | |
| Feb 18, 2023 at 10:38 | history | edited | Salvo Tringali | CC BY-SA 4.0 |
fixed a detail
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| Feb 18, 2023 at 10:22 | history | asked | Salvo Tringali | CC BY-SA 4.0 |