<content> OLD - Combinatorial </content>

27931f0e-eff7-47c2-92e3-7cfda3193b4c 133 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#) set_Settings_Orientation vertical : 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# 51 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# Co 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 set_Settings_Orientation vertical : 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 91 line :

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

Row Vector with n*n^r Variations with repetitions A# r# set_Permute n# A# length : 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 A# k# el : for for for 21 line for M# w# el V# w# col : set_Settings_Orientation vertical ≡ M# 1 w# el V# w# col transpose : cases 31 line :

Calculate the set of combinations, variations or permutations with or without repetitions. 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# 0 n# matrix eval : 12 mat set_Settings_Orientation vertical : x# u# x# : A# set_Cardinality n# ≡ x# u# x# set_Unique : cases x# Is# O# x# strrep strlen O# strlen < (: V# A# set_Permute u# : π Is# V# A# r# set_Permute u# : P Is# R Is# & a# A# set_Permute V# V# a# k# el 11 mat set_Union : for P Is# a# A# r# set_Permute V# V# a# k# el set_Sort 11 mat set_Union : for C Is# R Is# & V# A# r# set_Choose u# : C Is# Unknown option error cases M# 0 : c# 1 V# length range : 12 mat M# k# c# el V# c# el k# el : 21 line M Is# V# transpose cases 71 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 :

<content> Examples </content>

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

n r C n! n r - (! r! * / ≡

P MC 32 C : 11223323 mat

P set_Cardinality 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 set_Cardinality 10

53 C 10

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

P set_Cardinality 5

A set_Cardinality 4 C 5

Combinations with repetitions

n r CR n r + 1 - r C ≡

P MCR 32 C : 12312132313226 mat

P cols 6

32 + 1 - 2 C 6

P CR 43 C : 14431 mat 22231 mat 13431 mat 12231 mat 22431 mat 34431 mat 44431 mat 33431 mat 23431 mat 24431 mat 13331 mat 22331 mat 11231 mat 11131 mat 114 mat

P set_Cardinality 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 set_Cardinality 35

53 + 1 - 3 C 35

Variations

n r V n! n r - (! / ≡

P P 32 C : 2121 mat 1321 mat 3221 mat 1221 mat 2321 mat 3121 mat 16 mat

P set_Cardinality 6

2! 32 C * 6

P MP 43 C : 241213342314141342234132412132423143324431311224124321234431412124123343324 mat

P cols 24

3! 43 C * 24

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

P cols 20

2! A set_Cardinality 2 C * 20

Variations with repetitions

n r VR n r^≡

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 set_Cardinality 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 set_Cardinality 25

52^25

Permutations

n P n! ≡

P MP 3 C : 12312321133233221136 mat

P cols 6

3! 6

P P 4 C : 123441 mat 213441 mat 312441 mat 132441 mat 231441 mat 321441 mat 421341 mat 241341 mat 142341 mat 412341 mat 214341 mat 124341 mat 134241 mat 314241 mat 114 mat

P set_Cardinality 24

4! 24

P MP A C : a b c a b c d b a d b a a c d a c d d c b d c b ε b a a c c b b d d a a b c a a d d c c d d b b c c c c b b a a a a b b d d d d c c a a b b c c d d d d d d d d d c c c c c c b b b b b b a a a a a a a ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε b 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 b a a a b b b a a c c b b c 35 mat

P cols 5

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

P cols 10

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

P cols 18

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

P cols 27

P MP B C : b a c a a b b b a c a a a c b b b c a a b a b a b c c b a b a a b b b a b c a a c b c a a a b b b a a b c c c b a b b a a b a a b b a a c a a c b b c b a b b b a a b b a a b c c c c c a c c c c a b b b a a a a a a a a b b b a b b b b a b b b b b b a a a b b b b b b b b c c a c c c c a a a a a a a a 530 mat

P cols 30

Further things

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

C B r C CR B r C set_SymmetricDifference b c c 31 mat a a a 31 mat c c c 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 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 2321 mat 1421 mat 1221 mat 3121 mat 2121 mat 4121 mat 3221 mat 1321 mat 18 mat

Alvaro

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