A plane partition which is invariant under permutation of the three axes and which is equal to its complement (i.e., the collection of cubes
that are in a given box but do *not* belong to the solid Young diagram). The
number of totally symmetric self-complementary plane
partitions is the same as that for alternating
sign matrices and descending plane partitions.

# Totally Symmetric Self-Complementary Plane Partition

## See also

Alternating Sign Matrix, Descending Plane Partition, Plane Partition## Explore with Wolfram|Alpha

## References

Bressoud, D. and Propp, J. "How the Alternating Sign Matrix Conjecture was Solved."*Not. Amer. Math. Soc.*

**46**, 637-646.

## Referenced on Wolfram|Alpha

Totally Symmetric Self-Complementary Plane Partition## Cite this as:

Weisstein, Eric W. "Totally Symmetric Self-Complementary Plane Partition." From *MathWorld*--A Wolfram Web Resource.
https://mathworld.wolfram.com/TotallySymmetricSelf-ComplementaryPlanePartition.html