[seqfan] A construction problem

Christopher Hunt gribble cgribble263 at btinternet.com
Fri Oct 28 11:34:25 CEST 2011


Dear Seqfans,

Let a(n) be the number of plane partitions that can be derived from a linear

(ordinary) partition comprising n distinct parts.

Let these parts be labelled a, b, c, d, ... with a > b > c > d ..., then

a(n) = 1, 2, 4, 11, 26, 74, 198 ., not in the OEIS.

The number of different 2D shapes is the number of linear partitions on n.

Plane partitions are such that its parts are non-increasing along rows and

down columns.

For example, the possible plane partitions that can be derived from "a b c
d"

are listed below.

 

a b c d

 

a c d

b

 

a b d

c

 

a b c

d

 

a c

b d

 

a d

b c

 

a b

c d

 

a d

b

c

 

a c

b

d

 

a b

c

d

 

a

b

c

d

 

Does anyone know of an algorithm, program or package that can generate

these "orderings"?

Is this linked to any other area of combinatorics?

 

Thanks,

Chris Gribble

 

 

 

 

 




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