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combinat

  

rankcomb

  

compute the lexicographic rank of a given combination

  

unrankcomb

  

compute the combination with a given lexicographic rank

 

Calling Sequence

Parameters

Description

Thread Safety

Examples

Compatibility

Calling Sequence

rankcomb( s, n )

unrankcomb( r, n, k )

Parameters

s

-

set(posint); a set of positive integers from 1 to n for some n

n

-

posint; size of the set from which combination members are chosen

k

-

posint; size of the combination

r

-

posint; the rank of a combination

Description

• 

Given a combination (subset) s of the integers from 1 to n, for some positive integer n, the command rankcomb( 's', 'n' ) computes the lexicographic rank of s.  That is, if s has k members, and if the k-subsets of {1,2,...,n} are listed lexicographically, then the position of the given subset in this ordered list is returned.

• 

Given a rank r (where r is at most binomial(n,k)), the command unrankcomb( 'r', 'n', 'k' ) computes the k-subset of {1,2,...,n} which occurs in the r-th place in a lexicographically ordered list of the k-subsets of {1,2,...,n}.

• 

The commands rankcomb and unrankcomb are inverse to one another in the sense that they satisfy rankcomb( unrankcomb( r, k, n ), n ) = r and unrankcomb( rankcomb( s, n ), nops( s ), n ) = s.

Thread Safety

• 

The combinat[rankcomb] and combinat[unrankcomb] commands are thread-safe as of Maple 16.

• 

For more information on thread safety, see index/threadsafe.

Examples

withcombinat:

rankcomb2,3,4,5

7

(1)

rankcomb2,3,4,9

29

(2)

unrankcomb29,9,3

2,3,4

(3)

Compatibility

• 

The combinat[rankcomb] and combinat[unrankcomb] commands were introduced in Maple 16.

• 

For more information on Maple 16 changes, see Updates in Maple 16.

See Also

combinat

combinat[choose]

 


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