Timeline for Examples when quantum $q$ equals to arithmetic $q$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 31 at 16:25 | comment | added | Timothy Chow | Related: Are binomial coefficients $F_1$ analogs of $q$-binomial coefficients? | |
| Mar 23 at 2:22 | comment | added | Sam Hopkins | @TimothyChow: to me “bare linear algebra” over $\mathbb{F}_1$ is the theory of finite sets, their subsets, etc. as one develops in elementary combinatorics. I think it’s true that number theorists want to do more than bare linear algebra over $\mathbb{F}_1$ (e.g. they want to keep track of the Frobenius automorphism, they want to do algebraic geometry, …) but that doesn’t mean it’s not “the same” $\mathbb{F}_1$. | |
| Mar 23 at 1:17 | comment | added | Timothy Chow | I thought of this too, but I think it may not answer the OP's question. Here's another way to phrase what I think is the intended question. In how many of these examples from algebraic combinatorics does the $q\to 1$ limit tie in with what number theorists think of as $\mathbb{F}_1$? That is, the $q$ arising in algebraic combinatorics is often visibly related to quantization, but it's often not so obviously related to $\mathbb{F}_1$. | |
| Mar 22 at 15:58 | history | edited | Sam Hopkins | CC BY-SA 4.0 |
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| Mar 22 at 15:55 | comment | added | Ira Gessel | For an explanation of the connection between $q$ as a variable and as a prime power in $q$-binomial coefficients, see D. E. Knuth's paper, Subspaces, subsets, and partitions, doi.org/10.1016/0097-3165(71)90022-7. | |
| Mar 22 at 13:39 | history | edited | Sam Hopkins | CC BY-SA 4.0 |
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| Mar 22 at 12:16 | history | answered | Sam Hopkins | CC BY-SA 4.0 |