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# Name:Treasa Bency Biju Jose
# Date: 11/19/2020
# Assignment #21
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1. L := WtEdConGclever(50, a);
coeff(L[50], a, 70);
          [Length of output exceeds limit of 1000000]

5575701252629362995520950514528328589519583069523923795527195167\

  48979534894703561052813706583449695070191616000000

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3. 
FindCutOff(30, 1.05);
                               84
EstimateCutOff(30, 1000);
                               29
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5. 
EstProbKcomps := proc(n, m, k, N) local i, co, G; 
co := 0; 
for i to N do 
  G := RandGr(n, m); 
  if nops(CCs(G)) = k then 
    co := co + 1; 
  end if; 
end do; 
evalf(co/N); 
end proc;


EstProbKcomps(30, 70, 1, 100);
                          0.8600000000

EstProbConn(30, 70, 100);
                          0.8800000000
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6. 
WtEdKConGclever := proc(N, a, k) local f, i, x; option remember; 
f := log(Sum((a + 1)^(1/2*n*(n - 1))*x^n/n!, n = 0 .. infinity))^k/k!; 
f := taylor(f, x = 0, N + 1); 
[seq(expand(coeff(f, x, i)*i!), i = 1 .. N)]; 
end proc;

ProbKcomponents := proc(n, m, k) local a; 
evalf(coeff(WtEdKConGclever(n, a, k)[n], a, m)/binomial(1/2*n*(n - 1), m)); 
end proc;


EstProbKcomps(40, 50, 2, 300);
                         0.09666666667

ProbKcomponents(40, 50, 2);
                         0.09801230118

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