Are there some references about tropical cluster algebras and tropical Laurent phenomenon? I searched on Google but only found one paper: Tropical Plucker functions and their bases .
Thank you very much.
$\begingroup$
$\endgroup$
asked Jan 11, 2017 at 14:41
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
Let me suggest Lauren Williams and my paper as a starting point:
David Speyer and Lauren Williams, MR 2164397 The tropical totally positive Grassmannian, J. Algebraic Combin. 22 (2005), no. 2, 189--210.
It's earlier than a lot of the other references mentioned, so it isn't as sophisticated but, for that reason, it is a lot more concrete.
answered Jan 11, 2017 at 16:28
$\begingroup$
$\endgroup$
2
There are certainly things related to tropical cluster algebras associated to surfaces. See Fomin, Shapiro, Thurston, https://arxiv.org/pdf/math/0608367, especially section 9.5, and the sequel by Fomin and Thurston, https://arxiv.org/abs/1210.5569, sections 14 and 15.
There is also work by Fock and Goncharov along similar lines, see for example https://arxiv.org/abs/math/0510312. (Note that this is much more accessible than some of their work!)
-
$\begingroup$ thank you very much for the references. It seems that they didn't mention the tropical Laurent phenomenon in these papers? $\endgroup$ Commented Jan 11, 2017 at 15:07
-