Timeline for Generalization of an up, left, right path problem
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 26, 2017 at 0:43 | comment | added | Jeremy Dover | Thanks to all who contributed! I have put up a draft OEIS sequence as A292878...hopefully will be published shortly. Please don't hesitate to mark up that sequence with new information. | |
| Sep 25, 2017 at 10:35 | vote | accept | Jeremy Dover | ||
| Sep 24, 2017 at 23:40 | comment | added | Jeremy Dover | @AnthonyQuas: Thanks for the suggestion, both in name and generalization. My origimal thought was to "reset" directions based on an "up" only, but I like the idea of ordering the dimensions. Thanks! | |
| Sep 24, 2017 at 22:52 | comment | added | Jeremy Dover | @MaxAlekseyev: I plan to do this. I just wanted to gather more information first. Thanks! | |
| Sep 24, 2017 at 22:22 | comment | added | Jeremy Dover | @JeanMarieBecker: sure...here is the link math.stackexchange.com/questions/2441318/… | |
| Sep 24, 2017 at 22:16 | comment | added | Jean Marie Becker | @Jeremy Dover Could you indicate the Math.StackExchange question you are refering to ? | |
| Sep 24, 2017 at 19:17 | answer | added | Jay Pantone | timeline score: 6 | |
| Sep 24, 2017 at 18:52 | comment | added | Anthony Quas | PS: The reason it's ballistic is that unlike regular random walk, this one moves away from the origin (in the $e_1$ direction at a linear rate); the reason it's iterated is that between steps of the $e_i$ direction, it performs a $(d-i)$-dimensional random walk in the remaining directions. | |
| Sep 24, 2017 at 18:51 | comment | added | Anthony Quas | This is absolutely not an answer to your question, but I have a suggested name: iterated ballistic random walk. A possible generalization (maybe this is what you had in mind?): once you move backwards or forwards in the $i$th direction, the reverse move in the $i$th direction is forbidden until after the walk has moved in the $(i-1)$st direction. This condition is also sufficient to ensure that there are no self-intersections. Again, there will be a simple recurrence relation to compute the number of walks because the process is driven by a Markov chain. | |
| Sep 24, 2017 at 13:38 | comment | added | Max Alekseyev | Please add the sequence to the OEIS. | |
| Sep 24, 2017 at 1:55 | history | asked | Jeremy Dover | CC BY-SA 3.0 |