Timeline for Q-binomials at roots of unity
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 28, 2020 at 5:12 | vote | accept | Per Alexandersson | ||
| May 28, 2020 at 5:12 | answer | added | Per Alexandersson | timeline score: 1 | |
| Sep 13, 2017 at 13:14 | comment | added | Ira Gessel | @PerAlexandersson I don't think so, but every root of unity is a primitive root of unity. | |
| Sep 12, 2017 at 7:08 | comment | added | Per Alexandersson | @IraGessel Is there a generalization of the q-Lucas theorem that does not assume a primitive root of unity? | |
| Sep 11, 2017 at 23:40 | comment | added | Ira Gessel | To give credit where credit is due, the $q$-Lucas theorem was first published, as far as I know, by Gloria Olive, Generalized powers, Amer. Math. Monthly 72 (1965), 619–625, equation (1.2.4). (The proof, which is not difficult, is apparently in her 1963 Ph.D. thesis, which I have not seen.) The theorem has been rediscovered many times since then, but I have not come across any earlier occurrence of it. | |
| Sep 9, 2017 at 20:57 | comment | added | Richard Stanley | You can put $q=\exp(2\pi ir/N)$ in the $q$-binomial theorem (say as stated in equation (1.87) of Enumerative Combinatorics, second ed.) and equate coefficients of $x^k$ to get an answer. A special case is Exercise 1.98. | |
| Sep 9, 2017 at 19:36 | comment | added | KConrad | A partial answer is in Theorem 2.5 of math.uconn.edu/~kconrad/articles/qmahler1.pdf, although I see that the previous comment covers the same cases. | |
| Sep 9, 2017 at 18:08 | comment | added | Martin Rubey | Is the $q$-Lucas theorem (see, eg. Lemma 3.1 in arxiv.org/pdf/1101.1020.pdf) of any help? | |
| Sep 9, 2017 at 17:23 | comment | added | John Machacek | I figure you may be aware, but perhaps the comment will be interesting and relevant to others. It's an interesting question. I am not sure what can be said about other cases. | |
| Sep 9, 2017 at 17:21 | comment | added | Per Alexandersson | @JohnMachacek: Right - this is actually the reason I am asking the question - for an application with CSP. My problem does not fall into the classical cases in the text you are referring to, unfortunately. | |
| Sep 9, 2017 at 17:09 | comment | added | John Machacek | Cyclic sieving gives some values. See Theorem 1.1. | |
| Sep 9, 2017 at 16:35 | history | asked | Per Alexandersson | CC BY-SA 3.0 |