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The original source would be Fomin-Zelevinsky, https://arxiv.org/abs/hep-th/0111053. Note that, for them, the "associahedron" is really just a fan (the normal fan to the simple polytope associahedron …

Proposition 4 of Morelli's paper "Pick's Theorem and the Todd class of a toric variety" gives a sufficient condition: it describes a setting in which there is a positive formula for coefficient of $x^ …

Two references, neither of which exactly addresses your question, are as follows: Ringel, Claus Michael Exceptional modules are tree modules. Linear Algebra Appl. 275/276 (1998), 471–493. In this p …

I think the answer is "no". Let's consider $p=2,d=3$. Suppose that we have a necklace which can be fairly divided using only 2 cuts (one less than the maximum number that may be required). Let …

The fan Hales is using is called the "face fan" of the polytope. In toric varieties, one mainly considers the outer normal fan of a polytope, which has a ray for each facet (perpendicular to it). …

Let $Q$ be a quiver without loops (cycles of length 1). Kac proved that if $K$ is algebraically closed, the dimension vectors of indecomposable representations of $Q$ over $K$ are exactly the positiv …

As a module over $kQ$, a finite-type preprojective algebra is a direct sum of each of the indecomposable $kQ$-modules once. Thus, the total dimension is the sum over all positive roots of the height …

Reflection functors take you between categories of representations of different orientations of the same quiver and preserve indecomposability (up to the fact that a reflection functor destroys a sing …

There is relevant information here, including a statement of the conjecture (as Conjecture 5.1). http://www.math.uni-bonn.de/people/schroer/fd-problems-files/FD-RigidModulesConj.pdf That preprint …

What is a good reference for cluster algebras from surfaces, with a view to their connection to Teichmuller theory? In my view, that means it should start off with unpunctured surfaces (and in fact …

Dag has already answered the case where the quiver is finite and acyclic, and given a conjecture in the case that cycles are allowed. I will prove his conjecture. Suppose we have an element $x$ of …

This sounds wrong to me. I think $D^b(Q)$ should be replaced by the derived category of finite length modules over the corresponding preprojective algebra of affine type. Homological mirror symmetry …

One simple answer is to talk about the totally positive part of $(G_{k,n})_{> 0}$, the part of the Grassmannian where all the maximal minors (=Plücker coordinates) are real and positive. Naively, if …

Ben Webster gave an introductory symplectic geometry course this past term which I think was very good. The presentation was pretty elementary. The course was offered through the Fields Institute, and …