PalomarSolution

Chip firing, graph divisors, and their combinatorial properties.

theorem ChipFiring.Propositions.riemann_roch {G : CFGraph} (h_conn : graphConnected G) (D : CFDiv G) (r rdual : ℤ) : rankEq G D r → rankEq G (canonicalDivisor G - D) rdual → r - rdual = deg D + 1 - genus G

theorem ChipFiring.Propositions.clifford {G : CFGraph} (h_conn : graphConnected G) (D : CFDiv G) (r rdual : ℤ) : rankEq G D r → rankEq G (canonicalDivisor G - D) rdual → 0 ≤ r → 0 ≤ rdual → ↑r ≤ ↑(deg D) / 2