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combinat

  

encodepart

  

compute canonical integer representing partition

  

decodepart

  

compute canonical partition represented by integer

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

encodepart(l)

decodepart(n, m)

Parameters

l

-

partition; non-decreasing list of positive integers

n

-

positive integer

m

-

positive integer

Description

• 

The functions encodepart and decodepart provide a canonical labeling of all the partitions of n.

• 

Given a partition l of n, encodepart(l) computes and returns the integer m between 1 and numbpart(n) uniquely representing this partition.

• 

Given a positive integer n and a positive integer m between 1 and numbpart(n) the function decodepart(m, n) computes and returns the unique partition l represented by this positive integer.

• 

The command with(combinat,encodepart) allows the use of the abbreviated form of this command.

Examples

withcombinat:

partition3

1,1,1,1,2,3

(1)

decodepart3,1

1,1,1

(2)

decodepart3,2

1,2

(3)

decodepart3,3

3

(4)

encodepart1,2

2

(5)

See Also

combinat[inttovec]

combinat[nextpart]

combinat[numbpart]

combinat[partition]

combinat[prevpart]

combinat[vectoint]