Timeline for Tanglegrams and functional equations of M. Somos
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 4, 2022 at 18:22 | history | edited | T. Amdeberhan | CC BY-SA 4.0 |
deleted 5 characters in body
|
| Jan 24, 2022 at 18:34 | vote | accept | T. Amdeberhan | ||
| Jan 24, 2022 at 18:22 | comment | added | Ira Gessel | @TAmdeberhan Yes, if $q$ is not a prime then the number $a_q(n)$ as defined are not integers. The “right” analogue of Michael Somos's equation when $q$ is a power of the prime $p$ is $$A_q(x)^q = \frac{A(x^p)^{q/p}}{1-qxA(x^p)^{q/p}}.$$ (We also require that $A_q(0)=1$.) The coefficients of $A_q(x)$ defined this way are integers. | |
| Jan 24, 2022 at 17:46 | comment | added | T. Amdeberhan | Thank you for the answer here. Hope to read the promised proofs in your upcoming paper, soon. On the other hand, do you agree that $a_q(n)$ need not be integers when $q$ is a power of a primes. I checked with $q=2^2$ and they reveal rational numbers. | |
| Jan 24, 2022 at 5:02 | history | edited | Ira Gessel | CC BY-SA 4.0 |
deleted 28 characters in body
|
| Jan 23, 2022 at 22:14 | history | edited | Ira Gessel | CC BY-SA 4.0 |
added 49 characters in body
|
| Jan 23, 2022 at 19:16 | history | answered | Ira Gessel | CC BY-SA 4.0 |