TOÁN RÒ I RA C Pha m Tiến So n D à La t, 2005 2 Mu c lu c MO ’̇ D À̂U 6 1 PHÉP D É̂M 9 1 1 Các nguyên lý co bȧ’n cu̇’a phép d̄ếm 9 1 1 1 Nguyên lý tô̇’ng 9 1 1 2 Nguyên lý t́ıch 10[.]
´ RO `.I RA TOAN C Pha.m Tiˆe´n So.n - `a La.t, 2005 D Mu.c lu.c ˙’ D ˆU -` MO A ´ D ˆ´M -E PHEP C´ac nguyˆen l´ y co ba˙’n cu˙’a ph´ep d¯ˆe´m 1.1.1 Nguyˆen l´ y tˆo˙’ng 1.1.2 Nguyˆen l´ y t´ıch 10 1.1.3 Nguyˆen l´ y bao h`am-loa.i tr` u 13 1.2 Ho´an vi v`a tˆo˙’ ho p 15 1.3 C´ac thuˆa.t to´an sinh ho´an vi v`a tˆo˙’ ho p 20 1.4 Ho´an vi v`a tˆo˙’ ho p suy rˆo.ng 25 1.5 C´ac hˆe sˆo´ nhi th´ u.c v`a c´ac d¯`oˆng nhˆa´t th´ u.c 32 1.6 `ong chim bˆ `o cˆau Nguyˆen l´ y chuˆ 36 1.6.1 `ong chim bˆ `o cˆau (da.ng th´ Nguyˆen l´ y chuˆ u nhˆa´t) 36 1.6.2 `ong chim bˆ `o cˆau (da.ng th´ Nguyˆen l´ y chuˆ u hai) 37 1.6.3 `ong chim bˆ `o cˆau (da.ng th´ Nguyˆen l´ y chuˆ u ba) 39 1.1 ˆ QUAN HE 43 2.1 Quan hˆe hai ngˆoi 43 2.2 Quan hˆe v`a ma trˆa.n 48 2.3 Quan hˆe th´ u tu 54 2.4 Quan hˆe tu.o.ng d¯u.o.ng 62 2.5 Bao d¯o´ng cu˙’a quan hˆe 69 2.6 Lattice cu˙’a c´ac phˆan hoa.ch 75 2.6.1 Thuˆa.t to´an giao c´ac phˆan hoa.ch 77 2.6.2 Thuˆa.t to´an trˆo.n c´ac phˆan hoa.ch 78 ˆ´ BOOLE -A D I SO 81 3.1 Lattice 81 3.2 Latiice phˆan bˆo´ 90 3.3 - a.i sˆo´ Boole D 96 3.4 H`am Boole 3.5 Biˆe˙’u diˆ˜en c´ac h`am Boole qua hˆe tuyˆe˙’n, hˆo.i v`a phu˙’ d¯.inh 107 3.6 Biˆe˙’u diˆ˜en tˆo´i thiˆe˙’u cu˙’a h`am Boole 111 103 3.6.1 Kh´ai niˆe.m 111 3.6.2 Phu.o.ng ph´ap ba˙’n d¯`ˆo Karnaugh 112 ˜ TUYE ˆ´N T´INH MA 4.1 119 Mo˙’ d¯`aˆu 119 4.1.1 Kh´ai niˆe.m 119 4.1.2 M˜a ph´at hiˆe.n lˆo˜i 120 4.1.3 M˜a su˙’.a sai 121 4.2 C´ac kh´ai niˆe.m 122 4.3 Khoa˙’ng c´ach Hamming 131 4.4 Hˆo.i ch´ u.ng 139 4.4.1 Gia˙’i m˜a d` ung ba˙’ng chuˆa˙’n 140 4.5 M˜a ho`an ha˙’o 143 4.6 M˜a Hamming 146 ˆ THI -` D O 149 5.1 C´ac kh´ai niˆe.m 149 5.2 `en v`a chu tr`ınh 154 Dˆay chuyˆ 5.3 Chu tr`ınh Hamilton v`a b`ai to´an ngu.`o.i du li.ch 162 5.4 5.3.1 Quy tˇa´c t`ım chu tr`ınh Hamilton 164 5.3.2 M˜a Gray 166 - u.`o.ng d¯i v`a ma.ch 169 D 5.4.1 5.5 Thuˆa.t to´an 171 Ma trˆa.n biˆe˙’u diˆ˜en d¯`oˆ thi 173 5.5.1 `e 173 Ma trˆa.n kˆ 5.5.2 Ma trˆa.n liˆen thuˆo.c 175 5.6 - ˇa˙’ng cˆa´u gi˜ D u.a c´ac d¯`ˆo thi 179 5.7 - `ˆo thi phˇa˙’ng 181 D ˆ CAY 6.1 6.2 6.3 191 Mo˙’ d¯`aˆu 191 6.1.1 C´ac kh´ai niˆe.m 191 6.1.2 M˜a Huffman 192 Cˆay bao tr` um 197 6.2.1 `eu rˆo.ng x´ac d¯.inh cˆay bao tr` Thuˆa.t to´an t`ım kiˆe´m theo chiˆ um 198 6.2.2 `eu sˆau x´ac d¯i.nh cˆay bao tr` Thuˆa.t to´an t`ım kiˆe´m theo chiˆ um 199 Cˆay bao tr` um nho˙’ nhˆa´t 200 6.3.1 Thuˆa.t to´an Kruskal 201 T` liˆ e.u tham kha˙’o [1] C Berge, L´y thuyˆe´t d¯`ˆ o thi v` au ´.ng du.ng, NXB Khoa ho.c v`a k˜ y thuˆa.t H`a Nˆo.i, 1971 [2] A Cayley, Collected papers, Quart Jl of Mathematics, 13 Cambridge, 26 (1897) [3] N Biggs, Discrete mathematic, Clarendon Press Oxford, 1989 [4] Dijkstra, E W., A note on two problems in connection with graphs, Numerische Mathematik, 1, 269 (1959) [5] P J Cameron, Combinatorics: topics, techniques, algorithms, Cambridge University Press, 1994 [6] N Deo, Graph theory with applications to engineering and computer science, PrenticeHall Inc., 1974 [7] R J MC Eliece, M Kac, The theory of information and coding, Addison-Wesley, 1977 [8] C M Goldie, R G E Pinch, Communication theory, Cambridge University Press, 1991 [9] R W Hamming, Coding and information theory, Prentice Hall, 1980 [10] R Hill, A first course in coding theory, Clarendon Press Oxford, 1985 [11] R Johnsonbaugh, An introduction to discrete mathematic, Macmillan Publishing Company, 1992 [12] A R Kenneth, C R.B Wright, Discrete mathematics, Prentice-Hall International Editions, 1978 [13] Kirchhoff G., in “Annalen der Physik and Chemie” 72, 497 (1847) [14] S Lipschutz, Essential computer mathematic, McGraw-Hill, 1992 [15] S Lipschutz, M L Lipson,2000 sloved problems in discrete mathematics, McGraw-Hill, 1992 [16] C L Liu, Introduction to combinationnal mathematic, McGraw-Hill, 1985 215 [17] F J MacWilliams, N J A Soane, The theory of error-correcting codes, North-Holland, 1981 [18] A A Michael, A J Kfoury, R N Moll, D Gries, A basis for theoretical computer science, Springer-Verlag NewYork Inc., 1981 [19] J G Michaels, K H Rosen, Applications of discrete mathematics, McGraw-Hill, 1991 [20] Prim R C., Shortest connection networks and some generalizations, Bell Syst Tech Jl., 36, 1389 (1957) [21] S Roman, An introduction to discrete mathematic, Saunders College, 1982 [22] K H Rosen, Discrete mathematics and its applications, McGraw-Hill, 1995 [23] B M Stephen, A Ralston, Discrete algorithmic mathematics, Addision-Wesley Publishing Company, 1991 [24] D Welsh, Codes and cryptography, Clarendon Press Oxford, 1987 216