# Counting Quiver Representations over Finite Fields Via Graph Enumeration

@article{Helleloid2008CountingQR,
title={Counting Quiver Representations over Finite Fields Via Graph Enumeration},
author={Geir T. Helleloid and Fernando Rodriguez Villegas},
journal={arXiv: Representation Theory},
year={2008}
}
• Published 2008
• Mathematics
• arXiv: Representation Theory
• Let $\Gamma$ be a quiver on n vertices $v_1, v_2, ..., v_n$ with $g_{ij}$ edges between $v_i$ and $v_j$, and let $\alpha \in \N^n$. Hua gave a formula for $A_{\Gamma}(\alpha, q)$, the number of isomorphism classes of absolutely indecomposable representations of $\Gamma$ over the finite field $\F_q$ with dimension vector $\alpha$. Kac showed that $A_{\Gamma}(\bm{\alpha}, q)$ is a polynomial in q with integer coefficients. Using Hua's formula, we show that for each non-negative integer s, the s… CONTINUE READING

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 12 REFERENCES
The On-Line Encyclopedia of Integer Sequences
4537
Counting Quiver Representations over Finite Fields Via Graph Enumeration, submitted, also available at arXiv:0810