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Results tagged with positivity
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user 10744
11
votes
Positivity of a one-variable rational function
The rational function $(1-z)/(1-2z+z^2-z^3)$ has positive coefficients because it's equal to
$$\frac{1}{1-z-\displaystyle\frac{z^3}{1-z}}.$$
- 17k
5
votes
Exponential of a specific hypergeometric series
This is really a comment, but it's too long.
Here's another way to look at this phenomenon that explains the connection with Lyndon words.
Let $L_{\bf n}$ be the number of Lyndon words that are perm …
- 17k
12
votes
Exponential of a specific hypergeometric series
Here's a sketch of a proof of a much more general result. For simplicity I'll consider only the 3-variable case, but clearly a similar result holds for any number of variables.
Let $\nabla$ be the op …
- 17k