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