Help For: Functions for counting representations of quivers
Function: numberofreps1,numberofreps2,numberofreps3 - compute numbers of representations of quivers over a finite field
aij - number of edges between vertices i and j in a graph
N - upper bound for the entries of the dimension vector
This program computes the number of isomorphism classes of representations, indecomposable representations and absolutely indecomposable representations of a quiver with up to three vertices over a finite field .
is a graph with up to three vertices.
These functions compute polynomials , and with less than or equal to simultaneously where
is the number of isoclasses of representations of (with an arbitrary orientation) over $ with dimension vector ,
is the number of isoclasses of indecomposable representations of (with an arbitrary orientation) over with dimension vector ,
is the number of isoclasses of absolutely indecomposable representations of (with an arbitrary orientation) over with dimension vector .
For the function numberofreps1 to work properly, the integer N is less than or equal 16, for numberofreps2 N is less than or equal 6 and for numberofreps3 N is less than or equal 4.
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