# [seqfan] Re: A construction problem

franktaw at netscape.net franktaw at netscape.net
Sat Oct 29 08:41:31 CEST 2011

```Your numbers are off. The correct values are:

1, 2, 4, 10, 26, 76, 232, ...

This is A000085, the number of involutions.

Replace your a with 1, b with 2, etc., and you will find that you are
counting what are known as Young tableaux.

a d
b c

is not legal, so a(4) = 10, not 11.)

-----Original Message-----
From: Christopher Hunt gribble <cgribble263 at btinternet.com>

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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```