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arXiv · 0903.1928

On the cardinalities of Kronecker quiver Grassmannians

Csaba Szántó
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Abstract

We deduce using the Ringel-Hall algebra approach explicit formulas for the cardinalities of some Grassmannians over a finite field associated to the Kronecker quiver. We realize in this way a quantification of the formulas obtained by Caldero and Zelevinsky for the Euler characteristics of these Grassmannians. We also present a recursive algorithm for computing the cardinality of every Kronecker quiver Grassmannian over a finite field.

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Csaba Szántó. 2009-09-24. On the cardinalities of Kronecker quiver Grassmannians. https://arxiv.org/abs/0903.1928

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