Timeline for "Upside-down unimodal" sequences in combinatorics
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 8, 2023 at 21:16 | comment | added | Sam Hopkins | I just learned that there is an arcsine law for a certain kind of lozenge tiling problem; see Theorem 3 of this paper of Fulmek and Krattenthaler: arxiv.org/abs/math/9712244. This should probably lead to another example of a combinatorially meaningful upside-down unimodal sequence. | |
| Oct 8, 2023 at 10:07 | answer | added | Martin Rubey | timeline score: 4 | |
| Oct 7, 2023 at 8:50 | answer | added | Alexander Burstein | timeline score: 1 | |
| Oct 6, 2023 at 3:05 | comment | added | Gerry Myerson | How about $a_r=2^n-{n\choose r}$, the number of subsets of an $n$-set, of size not equal to $r$? Too silly? | |
| Oct 5, 2023 at 16:09 | history | became hot network question | |||
| Oct 5, 2023 at 16:06 | answer | added | Peter Taylor | timeline score: 5 | |
| Oct 5, 2023 at 13:37 | comment | added | Peter Taylor | With respect to rarity, I'm still manually filtering OEIS sequences to ones which are at least tangentially related to combinatorics, but pre-manual-filtering there are about six times as many plausibly non-trivially unimodal as plausibly non-trivially upside-down unimodal sequences in OEIS. (My concept of non-trival here requires at least three descents and at least three ascents, and the "plausibly" disclaimer is because my code only looks at the terms of the sequence available in the database). | |
| Oct 5, 2023 at 13:03 | comment | added | Sam Hopkins | A speculation about the rarity of these upside-down sequences. Often a sequence of unimodal sequences will be "asymptotically normal," i.e. converge to the normal distribution. But if a sequence of upside-down unimodal sequences converges, it must be to some weirder, upside-down bell shape distribution. The $b_{n,k}$ example converges to something called the arcsine law, I beleive. | |
| Oct 5, 2023 at 12:57 | history | edited | Sam Hopkins | CC BY-SA 4.0 |
added 186 characters in body
|
| Oct 5, 2023 at 5:44 | answer | added | Chris McDaniel | timeline score: 6 | |
| Oct 4, 2023 at 23:11 | history | edited | Sam Hopkins | CC BY-SA 4.0 |
added 4 characters in body
|
| Oct 4, 2023 at 22:51 | history | asked | Sam Hopkins | CC BY-SA 4.0 |