On the Doubly Refined Enumeration of Alternating Sign Matrices and Totally Symmetric Self-Complementary Plane Partitions

T. Fonseca ¹, Paul Zinn-Justin ¹

The Electronic Journal of Combinatorics 15 (2008) R81

We prove the equality of doubly refined enumerations of Alternating Sign Matrices and of Totally Symmetric Self-Complementary Plane Partitions using integral formulae originating from certain solutions of the quantum Knizhnik–Zamolodchikov equation.

• 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE),
  CNRS : UMR7589 – Université Paris VI – Pierre et Marie Curie – Université Paris VII – Paris Diderot