Timeline for Why are negative sets multisets? (Reference request)
Current License: CC BY-SA 4.0
9 events
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| Mar 10, 2022 at 13:45 | history | edited | Vince Vatter | CC BY-SA 4.0 |
Put quote in quote environment
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| Apr 9, 2016 at 12:48 | comment | added | Todd Trimble | On the other hand, I'm very tempted to view this in terms of superalgebra, interpreting $\binom{n}{k}$ as [the dimension of] the $k$-th alternating power of an $n$-dimensional vector space in ordinary algebra, but when we apply the functorial construction to an $n$-dimensional super space concentrated in the odd component, we get a $k$-th symmetric power of the underlying space (concentrated in the component of parity $k$). | |
| Apr 9, 2016 at 0:51 | history | edited | Vince Vatter | CC BY-SA 3.0 |
Mixed multiset typesetting
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| Jun 16, 2013 at 18:03 | comment | added | Timothy Chow | I don't know the answer, but if you have not done so already, I'd recommend that you check the books "Discrete Thoughts" and "Indiscrete Thoughts". | |
| Jun 16, 2013 at 6:16 | answer | added | Mark | timeline score: -2 | |
| Jun 15, 2013 at 16:54 | comment | added | Sam Hopkins | This paper by D. Loeb, "Sets with a negative number of elements": faculty.uml.edu/jpropp/negative.pdf, has a reference to a paper that Loeb and Rota wrote together. Perhaps there is a clue there- I can't find it online, though. | |
| Jun 15, 2013 at 15:59 | comment | added | Gjergji Zaimi | I can't resist pointing out that this interpretation of "negative sets are multisets" is made very clear by the "Euler characteristic as generalized cardinality" point of view. In fact, since we know that $\chi (Sym^k X)=\binom{\chi(X)}{k}$, we notice that $\binom{n}{k}$ counts the number of ways of picking $k$ points among $n$ points, but on the other hand, $(-1)^k\binom{-n}{k}$ counts the number of ways of picking $k$ points among $n$ intervals (this is the same as multisets of size $k$). | |
| Jun 15, 2013 at 13:59 | answer | added | Lee Mosher | timeline score: 6 | |
| Jun 15, 2013 at 8:25 | history | asked | Vince Vatter | CC BY-SA 3.0 |