arXiv 2303.034662023-03-06math.COmath.ACmath.AG

F-Polynomials of Donaldson-Thomas Transformations

Daping Weng

备注：: 27 pages, 19 figures

英文摘要：

$F$-polynomials are integer coefficient polynomials encoding the mutations of cluster variables inside a cluster algebra. In this article, we study the $F$-polynomials associated with the action of Donaldson-Thomas transformations on cluster variables. For acyclic quivers, quivers of surface types, and quivers associated with triples of flags, we give explicit descriptions of their Donaldson-Thomas $F$-polynomials in terms of generating functions for ideals inside a labeled poset. We also describe the combinatorial procedure needed to modify these labeled posets to obtain Donaldson-Thomas $F$-polynomials for full subquivers and triangular extensions.

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