Timeline for Explicit expression for recursive sums
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 11, 2022 at 21:59 | comment | added | Peter Taylor | I've passed the buck to Irwin. I personally would be willing to add a comment about the equivalence but not to remove the word "conjecture", because I don't have a proof. | |
| May 11, 2022 at 20:25 | comment | added | Max Alekseyev | @BillyJoe: I've asked about the recurrence related to A016121 in a new question: mathoverflow.net/q/422322 | |
| May 11, 2022 at 20:21 | comment | added | Max Alekseyev | @PeterTaylor: Indeed. Would you mind to remove "conjecture" from Irwin's comment? | |
| May 11, 2022 at 19:49 | vote | accept | Max Alekseyev | ||
| May 11, 2022 at 17:52 | comment | added | Sam Hopkins | @MaxAlekseyev: well, as you can now see, Richard Stanley identified the relevant polytopes (the "Pitman-Stanley polytope") and indeed a lot is known about these. | |
| May 11, 2022 at 17:03 | answer | added | Richard Stanley | timeline score: 9 | |
| May 11, 2022 at 7:19 | comment | added | Peter Taylor | Irwin's conjecture on A107877 is equivalent to the earlier comment by Joerg Arndt, Apr 30 2011, which doesn't qualify it as a conjecture. | |
| May 11, 2022 at 2:58 | answer | added | Hugh Denoncourt | timeline score: 11 | |
| May 10, 2022 at 21:49 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
deleted 355 characters in body; added 2 characters in body; edited body
|
| May 10, 2022 at 21:43 | comment | added | Max Alekseyev | @BillyJoe: You're correct. I've messed it up with another recurrence (also quite intriguing): $$g_{k+1}(t_1,t_2,\dots,t_{k+1}) = \sum_{j=0}^{t_1} g_k(t_2+j, t_3+j, \dots, t_{k+1}+j).$$ | |
| May 10, 2022 at 21:08 | comment | added | Fabius Wiesner | Are you sure about A016121? Apparently $f_k(n,d,d,\ldots,d,d)=\frac{n+1}{k}\binom{n+k(d+1)}{k-1}$. | |
| May 10, 2022 at 17:49 | comment | added | Max Alekseyev | @BillyJoe: Nice catch! In fact, it is stated there as conjecture by Benedict W. J. Irwin. | |
| May 10, 2022 at 17:32 | comment | added | Fabius Wiesner | FWIW it seems that $f_k(1,2,3,\ldots,k-2,k-2,k)=a(k+1)$, where $a(k)$ is A107877. | |
| May 9, 2022 at 2:21 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
added 15 characters in body; deleted 2 characters in body
|
| May 9, 2022 at 2:20 | comment | added | Sam Hopkins | The equal arguments case looks like it should also give the Ehrhart polynomial of some lattice polytope. | |
| May 9, 2022 at 2:14 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
added 455 characters in body; added 80 characters in body
|
| May 8, 2022 at 21:41 | history | asked | Max Alekseyev | CC BY-SA 4.0 |