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August 7th, 2017, 01:24 PM  #1 
Senior Member Joined: Oct 2016 From: Arizona Posts: 107 Thanks: 25 Math Focus: Well... there are some open problems in Frame Theory that I'd like to work on.  cyclic sum question (wasn't sure what category to put in)
This is my first time encountering this type of a problem, so I am wondering if someone can help me understand what this means: Let $x, y$ and $z$ be positive real numbers and $k$ a nonnegative integer.... then it proceeds to give an inequality whose left side is the following cyclic sum. $\sum_{cyc}\frac{x^{2k+2}+y^{2k+2}}{z^{2k+1}}$ I just want to know if I'm getting this right. Is it implied that the $k$ is not cycling? Does the sum mean $\frac{x^{2k+2}+y^{2k+2}}{z^{2k+1}} + \frac{z^{2k+2}+x^{2k+2}}{y^{2k+1}}+ \frac{y^{2k+2}+z^{2k+2}}{x^{2k+1}}$? 
August 7th, 2017, 02:48 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,704 Thanks: 1804 
Yes, common sense indicates that it's x, y and z that cycle.

August 7th, 2017, 02:51 PM  #3 
Senior Member Joined: Oct 2016 From: Arizona Posts: 107 Thanks: 25 Math Focus: Well... there are some open problems in Frame Theory that I'd like to work on. 
That's what I thought, but am I right about what the cyclic sum means?

August 7th, 2017, 07:47 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,704 Thanks: 1804 
Yes.


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