Gog, Magog and Schützenberger II: left trapezoids

Abstract

We are interested in finding an explicit bijection between two families of combinatorial objects: Gog and Magog triangles. These two families are particular classes of Gelfand-Tsetlin triangles and are respectively in bijection with alternating sign matrices (ASM) and totally symmetric self complementary plane partitions (TSSCPP). For this purpose, we introduce left Gog and GOGAm trapezoids. We conjecture that these two families of trapezoids are equienumerated and we give an explicit bijection between the trapezoids with one or two diagonals.

Keywords

• gog
• magog triangles and trapezoids
• schützenberger involution
• alternating sign matrices
• totally symmetric self complementary plane partitions
• [info.info-dm]computer science [cs]/discrete mathematics [cs.dm]