Gog and Magog triangles, and the Schutzenberger involution

TL;DR

This paper presents a new bijection between Gog and Magog trapezoids with two diagonals using the Schutzenberger involution, contributing to the combinatorial understanding of these structures.

Contribution

It introduces an explicit bijection between Gog and Magog trapezoids with two diagonals based on the Schutzenberger involution.

Findings

Established a bijection between Gog and Magog trapezoids with two diagonals.

Connected the Schutzenberger involution to the combinatorial structures of Alternating Sign Matrices and plane partitions.

Enhanced understanding of the symmetry and relationships in combinatorial objects.

Abstract

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.