This is the accompanying worksheet for the paper
"Enumeration of Non-oriented maps via integrability"

This worksheet contains:
A - an implementation of the explicit recurrences of the paper in the form of ready to run programs.
B - automated calculations of the non-shifted ODEs stated in non-explicit form in the paper, and recursive programs obtained from them to compute the numbers
C - some sanity checks against already known sequences (small genus, one face, ...)
D -
explicit displays of the big ODEs if you are into this
E -
some tables

version of 22 Oct.  2021 


A- Built-in explicit recurrences (obtained from ODEs with shifts) 


The case of maps via the quadrangulation approach (Thm 1.1 and Thm 5.2) 

The case of  maps via our main approach (Thm 3.6) 

The case of bipartite maps (Thm 4.4)  

The case of triangulations (Thm 4.9)   




B- Automatic derivation of the non-shifted ODEs and derived programs. 

The case of maps: derivation and properties of the ODE (Prop 3.4, Thm 3.7, Thm 1.2, Cor 3.8) 

The case of maps: recursive program derived from ODE  

The case of bipartite maps: derivation of ODE  (Prop 3.4, Thm 4.5, Thm 4.6, Thm 4.7) 

The case of bipartite maps: recursive program derived from ODE 

The case of triangulations: derivation of the ODE (Prop 4.8, Thm 4.10, Thm 4.11)  

The case of triangulations: recursive program derived from ODE 




C - Tests and Sanity Checks 

Checks for maps  

Checks for triangulations   

Checks for bipartite maps   


D - explicit display of the big ODEs 

Maps   (Thm 3.7) 

Bipartite Maps  (Thm 4.5) 

Triangulations   (Thm 4.10)  



E - Some tables