#neworder.maple
interface(quiet=true):

##############################################################
#
#	This maple code computes the ranks of elements in the 
#	symmetric group in the new order. 
#
#	Frank Sottile
#	28 February 1997
#
###############################################################
with(combinat):

n:=11:

m := iquo(n*n, 4):

stat := array(1..m+1):

for jj from 1 to m+1 do: stat[jj]:=0 od:

pi:=[1]:

for j from 2 to n do: pi := [pi[],j]; od:

asc := 1:

while (asc > 0) do:

rank := 0:

up := {}:   
down := {};
for j from 1 to n do:
 if (j<pi[j]) then up:=up union {j} fi:
 if (j>pi[j]) then down:=down union {j} fi:
od:

for a in up do:   for b in down do:
if (pi[a]>pi[b]) then rank := rank +1  fi:
if (a>b) then rank := rank -1 fi:
od:od:

for a in up do:     for aa in up do:
if (a>aa and pi[a]<pi[aa]) then  rank := rank -1 fi:
od:od:

for a in down do:   for aa in down do:
if (a>aa and pi[a]<pi[aa]) then  rank := rank -1 fi:
od:od:

stat[rank+1] := stat[rank+1] +1:

w := eval(pi):

asc := 0;
for j from 1 to n-1 do:
if (pi[j]<pi[j+1]) then asc := j fi: od;

if (asc >0) then 
dummy := eval(pi[asc]);

for ii from asc+1 to n do:
if (pi[ii]>dummy) then bigger:=ii fi: od:

pi[asc]:= eval(w[bigger]):
w[bigger]:= dummy:

for jj from 1 to n-asc do;
pi[asc+jj]:= eval(w[n+1-jj]); od;

fi;
od:

print(stat);

quit

###################################