On the cardinalities of Kronecker quiver Grassmannians

Details On the cardinalities of Kronecker quiver Grassmannians On the cardinalities of Kronecker quiver Grassmannians

2009-03-11

arxiv.org/abs/0903.1928v2

Mathematics

Representation Theory

Major corrections and completions were made. We also present a recursive algorithm for computing the cardinality of every Kron

Scientific paper

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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