//Session file
SetLogFile("adj.log": Overwrite := true);

//adjacency counter
numADJ := function(sd);
   s := 0;
   n := #sd;
   for  i := 1 to n-1 do
        if  Abs(sd[i]-sd[i+1]) eq 1 then s := s+1; end if;
        end for;
   return s;
   end function;

//define deck, set up "shuffle group"
udeck := [1,2,3,4,5];
G := SymmetricGroup(5);

//average number of adjacencies
nadj := 0;
for pi in G do
    nadj := nadj+numADJ(udeck^(pi^(-1))); 
    end for;
avgADJ := nadj/#G;
print "avgADJ = " , avgADJ;

//probability of an adjacency
a := 0;
for pi in G do
    if numADJ(udeck^(pi^(-1))) gt 0 then a := a+1; end if; 
    end for;
probADJ := a/#G;
print "probADJ = ",probADJ;


//End Session
UnsetLogFile();