F-polynomial maximal-monomial conjecture

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Fix a positive integer nn, an nn-regular tree Tn\mathbb{T}_n, a vertex t0∈Tnt_0\in\mathbb{T}_n, and a skew-symmetrizable integer matrix B=(bi,j)B=(b_{i,j}). For each t∈Tnt\in\mathbb{T}_n and ℓ=1,…,n\ell=1,\dots,n, let Fℓ;tB;t0∈Z[u1,…,un]F_{\ell;t}^{B;t_0}\in\mathbb{Z}[u_1,\dots,u_n] be the associated FF-polynomial. F-polynomial maximal-monomial conjecture. Each polynomial Fℓ;tB;t0F_{\ell;t}^{B;t_0} has a unique monomial of maximal degree. Furthermore, this monomial has coefficient 11, and it is divisible by all the other occurring monomials. The source says this is equivalent to the constant-term conjecture, but gives no resolution status.

References

Primary source

Harm Derksen, Jerzy Weyman and Andrei Zelevinsky, “Quivers with potentials and their representations II: Applications to cluster algebras”, arXiv:0904.0676 (2010).

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