Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chip-firing based methods in the Riemann--Roch theory of directed graphs   Baker and Norine proved a Riemann--Roch theorem for divisors on undirected
graphs. The notions of graph divisor theory are in duality with the notions of
the chip-firing game of Bj\"orner, Lov\'asz and Shor. We use this connection to
prove Riemann--Roch-type results on directed graphs. We give a simple proof for
a Riemann--Roch inequality on Eulerian directed graphs, improving a result of
Amini and Manjunath. We also study possibilities and impossibilities of
Riemann--Roch-type equalities in strongly connected digraphs and give examples.
We intend to make the connections of this theory to graph theoretic notions
more explicit via using the chip-firing framework.

7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys