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> with(SF);

a list of [arm', leg', arm, leg] for each cell in mu

> appendages:=proc(mu) option remember;
local armp, legp, mup;
mup:=`SF/conjugate`(mu);
[seq(seq([armp,legp,mu[legp+1]-armp-1,mup[armp+1]-legp-1],
armp=0..mu[legp+1]-1),legp=0..nops(mu)-1)];
end:

> muqtpol:=proc(mu) local apnd;
apnd:=appendages(mu);
t^(2*convert(map(x->x[4],apnd),`+`))*
q^(2*convert(map(x->x[3],apnd),`+`))*(1-t)*(1-q)*
convert(map(x->1-q^x[1]*t^x[2],apnd[2..nops(apnd)]),`*`)*
convert(map(x->q^x[1]*t^x[2],apnd),`+`)/
convert(map(x->q^x[3] - t^(x[4]+1),apnd),`*`)/
convert(map(x->t^x[4] - q^(x[3]+1),apnd),`*`);
end:

> qtCat:=proc(n) local mu,out;
out:=0;
for mu in Par(n) do
out:=simplify(out+muqtpol(mu));
od;
end:

> qttab:=proc(EX) local i,j;
matrix([seq([seq(coeff(coeff(EX,q,i),t,j),i=0..degree(EX,q))],j=0..degree(EX,t))]);
end:
 
 
 
 

> qttab(qtCat(5));
 

>