Timeline for A monoid-structure on pairs of interlacing polynomials
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 22, 2015 at 11:54 | history | edited | Roland Bacher | CC BY-SA 3.0 |
correction of a minor orthographical mistake
|
| Dec 4, 2014 at 9:03 | comment | added | Roland Bacher | Indeed, the natural candidate associates to a sequence $P_0,P_1,\dots$ of interlacing polynomials the series $\sum_k\geq 0}P_k t^k/k!$ (where $t$ is an additional variable). This candidate does not work. I thought a little bit about different possible twists and convinced myself that it is hopeless. | |
| Dec 3, 2014 at 21:43 | comment | added | Aaron Meyerowitz | I can find counter-examples which show that the obvious thing for triples: $(P_1,Q_1,R_1)\cdot(P_2,Q_2,R_2)=(P_1P_2,P_1Q_2+P_2Q_1,P_1R_2+2Q_1Q_2+P_2R_1)$ can fail. Do you have a proof that nothing can work? I suppose having $(1,0,0)$ be the identity precludes something silly like changing the third component to $P_1Q_2'+P_1'Q_2+Q_1P_2'+P_2Q_1'.$ | |
| Dec 3, 2014 at 19:31 | comment | added | Per Alexandersson | This is quite interesting! Wonder how this plays together with the differential operator. | |
| Dec 3, 2014 at 17:39 | comment | added | Ryan Budney | As a monoid, it is an extension over polynomials with multipilcation, and fibre polynomials with addition. Off the top of my head I don't see an isomorphism with the product extension, but perhaps it is the product? I'm ignoring your interlacing condition for now, apologies. | |
| Dec 3, 2014 at 16:51 | history | edited | Abdelmalek Abdesselam | CC BY-SA 3.0 |
changed obvious typo: monomial->monoid
|
| Dec 3, 2014 at 14:59 | history | asked | Roland Bacher | CC BY-SA 3.0 |