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

T. Fonseca (1) , Paul Zinn-Justin (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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.

Domaines: Combinatoire [math.CO]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

T. Fonseca, Paul Zinn-Justin. On the Doubly Refined Enumeration of Alternating Sign Matrices and Totally Symmetric Self-Complementary Plane Partitions. The Electronic Journal of Combinatorics, 2008, 15, pp.R81. ⟨hal-00348926⟩