Gog and Magog triangles, and the Schützenberger involution

Hayat Cheballah (1, 2) , Philippe Biane (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 LIPN - Laboratoire d'Informatique de Paris-Nord

We describe an approach to finding a bijection between Alternating Sign Matrices and Totally Symmetric Self-Complementary Plane Partitions, which is based on the Schutzenberger involution. In particular we give an explicit bijection between Gog and Magog trapezoids with two diagonals.

Domaines: Combinatoire [math.CO]

Hayat Cheballah, Philippe Biane. Gog and Magog triangles, and the Schützenberger involution. Journal of Séminaire Lotharingien de Combinatoire, 2012, 66 (B66d), pp.1-20. ⟨hal-00600343⟩