A connection between alternating sign matrices and totally symmetric self-complementary plane partitions

The Equivalence between Enumerating Cycl

The Equivalence between Enumerating Cyclically Symmetric, Self-Complementary and Totally Symmetric, Self-Complementary Plane Partitions

✍ Mihai Ciucu 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 142 KB

We prove that the number of cyclically symmetric, self-complementary plane partitions contained in a cube of side 2n equals the square of the number of totally symmetric, self-complementary plane partitions contained in the same cube, without explicitly evaluating either of these numbers. This appea