<content> <p>Combinatorial</p> </content>

27931f0e-eff7-47c2-92e3-7cfda3193b4c 81 4 5 false false 0 0 decimal

Combinatorial utilities

Row Vector with n*n^r Variations with repetitions n r CPerms q 1 n range : V 0 : M 0 : w 1 n r^range : 14 mat h 1 r range c 0 : j 1 n h 1 -^range k 1 n range m 1 n r h -^range V h c c 1 + : el q k el : for for for 21 line for M 1 w el V w col : 31 line :

Row Vector with n*n! Permutations n CPerms r 1 n range : q r : M 0 : 13 mat c 1 n! range M 1 c el q r el : h n 1 - (1 range q h el q h 1 + el < break if for j h 1 + : k n : m n : 13 mat j k < q j el q k el 12 mat q k el q j el 12 mat : j j 1 + : k k 1 - : 12 mat 21 line while q m el q h el > m m 1 - : while q h el q m 1 + el 12 mat q m 1 + el q h el 12 mat : 61 line for M 31 line :

P# CU U#:set_Union(P#) U# P# 1 el 11 mat : M# 0 : c# 1 : 13 mat j# 2 : j# P# rows ≤ j# j# 1 + : U# P# j# el 1 findrows num2str 0 ≡ U# c# c# 1 + : el P# j# el : if for U# 41 line :

A function for eliminate duplictates without changing the given order of the elements

P# x# P# set_ElementOf x# P# set_ElementOf set_SetBuilder :

Q# P# P# set_Union :

O# X# r# C A# 1 X# range : n# X# : 12 mat X# GetType number ≡ A# X# : n# A# length : 12 mat cases k# 1 r# range : V# k# 11 mat : 12 mat x# Is# O# x# strrep strlen O# strlen < (: P# U# c# 1 P# cols range V# V# P# c# el k# el sort 11 mat set_Union : C Is# V# V# P# c# el k# el 11 mat set_Union : cases for V# transpose 21 line : V# n# CPerms : π Is# V# n# r# CPerms : P Is# R Is# & V# n# CPerms U# : P Is# V# n# r# CPerms U# : C Is# R Is# & V# n# CPerms U# : C Is# Unknown option error cases P# 0 : c# 1 V# cols range : P# c# el A# V# c# el el : 13 mat M# 0 : U# P# CU : c# 1 U# rows range : 13 mat M# k# c# el U# c# el k# el : M Is# P# transpose cases 81 line :

n# r# C n# IsString num2str 1 ≡ n# P π strrep r# r# r# GetType number ≡ r# length cases C n#! n# r# - (! r#! * / if 11 line :

Syntax

Opt n r C

where options are

C Combinations P Permutations R With\0020\Repetitions M As\0020\Matrix 42 mat

Opt n C

n r C

Examples

A a b c d ε 15 mat :

Combinations

P MC 32 C : 21133223 mat

P cols 3

32 C 3

P C 53 C : 12331 mat 12431 mat 12531 mat 13431 mat 13531 mat 14531 mat 23431 mat 23531 mat 24531 mat 34531 mat 110 mat

P cols 10

53 C 10

P C A 4 C : a c d ε 41 mat b c d ε 41 mat a b d ε 41 mat a b c d 41 mat a b c ε 41 mat 15 mat

P cols 5

54 C 5

Combinations with repetitions

P MCR 32 C : 12312132313226 mat

P cols 6

32 + 1 - 2 C 6

P CR 43 C : 14431 mat 22231 mat 13431 mat 11431 mat 22431 mat 34431 mat 44431 mat 33431 mat 23431 mat 24431 mat 13331 mat 22331 mat 12231 mat 11331 mat 114 mat

P cols 20

43 + 1 - 3 C 20

P CR A 3 C : c c c 31 mat b b ε 31 mat c c ε 31 mat a ε ε 31 mat b b c 31 mat b c d 31 mat a b b 31 mat a b d 31 mat b d ε 31 mat a d d 31 mat c d d 31 mat ε ε ε 31 mat c ε ε 31 mat 113 mat

P cols 35

53 + 1 - 3 C 35

Variations

P MP 32 C : 12313233221126 mat

P cols 6

3! 32 - (! / 6

P MP 43 C : 222111444333322342113144134234123124113414432232443443332442231121221311324 mat

P cols 24

4! 43 - (! / 24

P MP A 2 C : a a a a b b b b c c c c d d d d ε ε ε ε b c d ε a c d ε a b d ε a b c ε a b c d 220 mat

P cols 20

5! 52 - (! / 20

Variations with repetitions

P MPR 32 C : 11122233312312312329 mat

P cols 9

32^9

P PR 43 C : 11131 mat 11231 mat 11331 mat 11431 mat 12131 mat 12231 mat 12331 mat 12431 mat 13131 mat 13231 mat 13331 mat 13431 mat 14131 mat 14231 mat 114 mat

P cols 64

43^64

P PR A 2 C : a a 21 mat a b 21 mat a c 21 mat a d 21 mat a ε 21 mat b a 21 mat b b 21 mat b c 21 mat b d 21 mat b ε 21 mat c a 21 mat c b 21 mat c c 21 mat 113 mat

P cols 25

52^25

Permutations

P MP 3 C : 11223323131232312136 mat

P cols 6

3! 6

P P 4 C : 123441 mat 124341 mat 132441 mat 134241 mat 142341 mat 143241 mat 213441 mat 214341 mat 231441 mat 234141 mat 241341 mat 243141 mat 312441 mat 314241 mat 114 mat

P cols 24

4! 24

P MP A C : a a a a a a a a a a a a a a a a a a a a a a a a b b b b b b b c c c c c c d d d d d d ε ε ε ε ε ε a c c d d ε ε b b d d ε ε b b c c ε ε b b c c d d c d ε c ε c d d ε b ε b d c ε b ε b c c d b d b c d ε d ε c d c ε d ε b d b ε c ε b c b d c d b c b ε 525 mat

P cols 120

5! 120

Whith Repetitions in the given set

B a a b b c 15 mat :

r 3 :

P MC B r C : a a a a b a a b b b b c b c c 35 mat

P cols 5

P MCR B r C : b a b a a a a a c b b a b c a b a b c c b c c c b b a c c c 310 mat

P cols 10

P MP B r C : a a a a a a a b b b b b b b c c c c a a b b b c c a a a b b c c a a b b b c a b c a b a b c a c a b a b a b 318 mat

P cols 18

P MPR B r C : a a a a a a a a a b b b b b b b b b c c c c c c c c c a a a b b b c c c a a a b b b c c c a a a b b b c c c a b c a b c a b c a b c a b c a b c a b c a b c a b c 327 mat

P cols 27

Further things

P B r C C B r C set_Intersection transpose a b c 31 mat b b c 31 mat a b b 31 mat a a b 31 mat a a c 31 mat 15 mat

C B r C CR B r C set_SymmetricDifference transpose c c c 31 mat b c c 31 mat a a a 31 mat b b b 31 mat a c c 31 mat 15 mat

x y 21 mat PR 32 C set_ElementOf y 2 ≡ set_SetBuilder transpose 3221 mat 2221 mat 1221 mat 13 mat

x y 21 mat P 16 range 2 C set_ElementOf x y + 25 lele set_SetBuilder transpose 3121 mat 2321 mat 4121 mat 3221 mat 1321 mat 1221 mat 2121 mat 1421 mat 18 mat

Alvaro