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# Name:Treasa Bency Biju Jose
# Date: 09-16-2020
# Assignment #3

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I.

Bnk(10, 5)[20];
                 [0, 0, 0, 1, 1, 1, 1, 0, 1, 0]

MyChoose({1, 2, 3, 4, 5, 6}, 2)[5];
                             {1, 6}

MyPermsL([r, u, t, g, e, r, s])[100];
                     [r, u, s, t, e, r, g]

WtoS([1, 0, 0, 0, 1]);
                             {1, 5}
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II.

NuFP := proc(pi) local i, N; 
N := 0; 
	for i to numelems(pi) do 
		if pi[i] = i then 
			N := N + 1; 
		end if; 
	end do; 
return N; 
end proc:
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III. 

Der := proc(n) local p, t, N, i, S; 
p := combinat[permute](n); 
S := {}; 
if p = {} then 
	return 0; 
else for i to nops(p) do 
	t := p[i]; 
	N := NuFP(t); 
	if N = 0 then 
		S := S union {t}; 
	end if; 
end do; 
end if; 
return S; 
end proc:
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IV.
[seq(nops(Der(i)), i = 0 .. 8)];
             [1, 0, 1, 2, 9, 44, 265, 1854, 14833]

A number on OEIS: A000166
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V.

[seq(nops(Comps(i)), i = 1 .. 8)];
                 [1, 2, 4, 8, 16, 32, 64, 128]

No: of Compositions of n, nops(Comps(n)) = 2^(n-1)
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VI.

Proof: nops(Comps(n)) = 2^(n-1)

evalb(nops(Comps(1)) = 2^0);
                              true

evalb(nops(Comps(20)) = 2^19);
                              true

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