Mathematics desk | ||
---|---|---|
< July 30 | << Jun | July | Aug >> | August 1 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
In the article about Vincent's theorem it's written that "As in the case of Descartes' rule of signs if varab(p) = 0 it follows that ρab(p) = 0". Does the second direction also hold? That is, if ρab(p) = 0 it follows that varab(p) = 0?
This direction is important to me since I wish to perform binary search on the sign variation in order to find the roots in an interval, and the correctness of this alogrithm depends on whether both directions hold. 185.32.179.35 ( talk) 10:54, 31 July 2016 (UTC)
How many ways are there to go from a single corner of a hypercube tracing every edge exactly once and back to that corner passing through each vertex twice (initial point is start, passthrough once and end (assume the corner and the orientation is fixed)? Naraht ( talk) 20:06, 31 July 2016 (UTC)
So properly in Graph theory, the question is "How many Eulerian cycles are there in the hypercube graph Qr?" And we know that there is at least one by the theorems at Eulerian path#Constructing Eulerian trails and circuits and information on what is known about counts is at Eulerian_path#Counting_Eulerian_circuits. Which doesn't appear to be much...
Is there some standard notation for the function defined recursively by ?
That is, to find , start with y and perform the operation n times.
If then this is simply tetration, expressible for example by Knuth's up-arrow notation: . But I don't know how to denote the result when .
If there is no standard notation for this, what is the most concise way to describe some value by combining more elementary standard notation?
Thanks. -- Meni Rosenfeld ( talk) 22:21, 31 July 2016 (UTC)
Mathematics desk | ||
---|---|---|
< July 30 | << Jun | July | Aug >> | August 1 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
In the article about Vincent's theorem it's written that "As in the case of Descartes' rule of signs if varab(p) = 0 it follows that ρab(p) = 0". Does the second direction also hold? That is, if ρab(p) = 0 it follows that varab(p) = 0?
This direction is important to me since I wish to perform binary search on the sign variation in order to find the roots in an interval, and the correctness of this alogrithm depends on whether both directions hold. 185.32.179.35 ( talk) 10:54, 31 July 2016 (UTC)
How many ways are there to go from a single corner of a hypercube tracing every edge exactly once and back to that corner passing through each vertex twice (initial point is start, passthrough once and end (assume the corner and the orientation is fixed)? Naraht ( talk) 20:06, 31 July 2016 (UTC)
So properly in Graph theory, the question is "How many Eulerian cycles are there in the hypercube graph Qr?" And we know that there is at least one by the theorems at Eulerian path#Constructing Eulerian trails and circuits and information on what is known about counts is at Eulerian_path#Counting_Eulerian_circuits. Which doesn't appear to be much...
Is there some standard notation for the function defined recursively by ?
That is, to find , start with y and perform the operation n times.
If then this is simply tetration, expressible for example by Knuth's up-arrow notation: . But I don't know how to denote the result when .
If there is no standard notation for this, what is the most concise way to describe some value by combining more elementary standard notation?
Thanks. -- Meni Rosenfeld ( talk) 22:21, 31 July 2016 (UTC)