Son Nguyen

The octahedron recurrence and its relationship with alternating sign matrices has been widely studied. In 2001, another recurrence called cube recurrence was introduced by James Propp. In 2004, Carroll and Speyer constructed a combinatorial model to describe the cube recurrence called groves. In this research, we propose and characterize a new model called alternating sign triangles. We have found the necessary and sufficient properties of permutation triangles and some other properties of alternating sign triangles that are similar to those of alternating sign matrices.