countingMaps-nonoriented9.html

The case of bipartite maps: recursive program derived from ODE

> # Returns the generating polynomial of ROOTED maps with n edges
# with u/v/z marking white v./black v./faces
# Computation coefficient by coefficient from the non-shifted ODE:
# (not optimized, a variant of Newton iteration could probably be used instead)
bipmapsEdges:= proc(n)
option remember:
if n<1 then return 0:
elif n=1 then return u*v*z;
elif n=2 then return u^2*v*z+u*v^2*z+u*v*z^2+u*v*z;
else
eval(subs(eta(t)=a*t^(n)/2/n+add(bipmapsEdges(k)*t^(k)/2/k,k=1..n-1),bigODEbipartite)):
factor(series(%,t=0,n+10)):
coeff(%,t,n):
factor(solve(%,a)):
return %;
fi;
end:

> #Example: 5 edges
bipmapsEdges(5);

(3.4.1)

> # Uses the previous one to compute maps by edges and genus
# (not optimal AT ALL for small genus since all genera are computed for each size)
bipmapsEdgesGenus:= proc(n,g)
option remember:
if n<1 then return 0:
else
expand(subs(u=u/s,v=v/s,z=z/s,bipmapsEdges(n)*s^(n+2))):
# print(%);
return factor(coeff(%,s,2*g));
fi;
end:

> #Example: 5 edges, genus 1
bipmapsEdgesGenus(5,1);

(3.4.2)