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102年 - 102 國立中山大學_碩士班招生考試_資工系(甲組)：離散數學#105881

科目： 中山◆資工◆離散數學 | 年份：102年 | 選擇題數：0 | 申論題數：25

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所屬科目： 中山◆資工◆離散數學

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申論題 (25)

(a) there are no restrictions?
(b) he considers five of the programs higher in priority than the others and wants to process those five first?
(c) he first separates the programs into four of top priority, eight of lesser priority, and three of least priority, and he wishes to process the fifteen programs in such a way that the top-priority programs are processed first and the three programs of least priority are processed last?
(a) if there are no restrictions?
(b) ifthe languages should alternate?
(c) if all the Java books must be next to each other?
(d) ifall the C++ books must be next to each other and all the Java books must be next to each other?
(a)How many times will the 400th coin be turned over?
(b) Which coin(s) will be turned over as many times as the 400th coin?
(c)Please show two coins that will be turned over more than 18 times?
(a) if all cycles are identical in appearance, as are the cars, and we want to use up all the n spaces.
(b) if the motorcycles come in two distinct models and the compact cars come in three different colors, and we want to use up all the n spaces.
(c) if all cycles are identical in appearance and the compact cars come in three different colors, and empty spaces are allowed.
(a)Find the generating function for the number of integer solutions to the equation,

(b) The number of integer solutions to the above equation equals to the coeficient of 61e8af2e0cb5f.jpg of the above generating function. What is n?
(c) Please find the coefficient of xl00 in the above generating function.

(a)61e8af56312e5.jpg

(b)61e8af62b66af.jpg
(0)f(x)=1/(1-x)-x2.

(a)Let e, be the number of edges in the Hasse diagram for the partial order61e8b00ae2d8d.jpg. Please find a recurrence relation for 61e8b03547717.jpg and then solve the recurrence relation to get 61e8b02cbbf73.jpg

(b) Please find 61e8b086da75a.jpgthe number of vertices of the diagram in (a).
(a)Find all generators of the cyolic group (Z8 +).
(b)Find all generators of the cyelic group (Z5-{0}, *).
(c) If G is a cyclic group of order n, how many distinct generators does it have?
9. Please find an encryption function E: {1, 2, 3, ... 26} -＞ Z such that E(m1) + E(m2) = E(m1+m2) for every m1, m2 in {1, 2,3, ... ., 26} and please also find the decryption function corresponding to E.