# Riemann-Roch-theorem of Baker and Norine

From Egres Open

[math] \rm{rank}(D) − \rm{rank}(K_G − D) = \deg(D) + 1 − g [/math],

where

- [math]D[/math] is any divisor on graph [math]G[/math],
- [math]g = |E(G)|-|V(G)| + 1 [/math] (the
*genus*of the graph,) and - [math]K[/math] is the canoncial divisor of [math]G[/math], defined as [math]K_G(v) = d(v)-2 [/math].

## Remarks

- Baker and Norine
^{[1]}found and proved this theorem as a discrete analogue to the classical Riemann–Roch-theorem.

## References

- ↑ M. Baker, S. Norine,
*Riemann--Roch and Abel--Jacobi theory on a finite graph*, Advances in Mathematics (2007) DOI link, ArXiv Link