PeterBurbery/Combinatorics | Paclet Repository

PeterBurbery`Combinatorics`

SelectPermutations

SelectPermutations [list,crit]
	generates a list of all possible permutations of the elements in list satisfying crit .

SelectPermutations [list,n,crit]
	gives all permutations containing at most n elements satisfying crit .

SelectPermutations [list,{n},crit]
	gives all permutations containing exactly n elements satisfying crit .

SelectPermutations […,crit,m]
	gives at most m results.

Details and Options



Examples

(8)

Basic Examples

(2)

Select from the list {5,6,7,8,9} those permutations that form a prime when concatenating the digits:

In[1]:=

SelectPermutations

[{5,6,7,8,9},PrimeQ@*FromDigits]

Out[1]=

{{5,6,8,9,7},{5,7,6,8,9},{5,8,6,7,9},{5,8,9,6,7},{6,5,7,8,9},{6,7,5,8,9},{6,8,5,9,7},{6,9,8,5,7},{7,5,6,8,9},{7,5,8,6,9},{7,8,5,6,9},{8,6,5,7,9},{8,9,5,6,7},{8,9,6,5,7},{9,6,5,8,7},{9,6,8,5,7}}

Select permutations of length 3:

In[2]:=

SelectPermutations

[{5,6,7,8,9},{3},PrimeQ@*FromDigits]

Out[2]=

{{5,6,9},{5,8,7},{6,5,9},{7,6,9},{8,5,7},{8,5,9},{9,6,7}}

Select permutations with length 3—4:

In[3]:=

SelectPermutations

[{5,6,7,8,9},{3,4},PrimeQ@*FromDigits]

Out[3]=

{{5,6,9},{5,8,7},{6,5,9},{7,6,9},{8,5,7},{8,5,9},{9,6,7},{5,6,8,9},{5,8,6,7},{5,8,6,9},{5,8,7,9},{5,8,9,7},{5,9,8,7},{6,8,5,7},{7,5,8,9},{8,5,9,7},{9,5,8,7},{9,8,5,7}}

Select permutations for which the first two elements and the last elements add up to the same value:

In[1]:=