Year: 2024
Type: article
Abstract: Plane partitions in the totally symmetric self-complementary symmetry class (TSSCPPs) are known to be equinumerous with $$n\times n$$ n × n alternating sign matrices, but no explicit bijection is known. In this paper, we give a bijection from these plane partitions to $$\{0,1,-1\}$$ { 0 , 1 , - 1 } -matrices we call magog matrices, some of which are alternating sign matrices. We explore enumerative properties of these matrices related to natural statistics such as inversion number and number of negative ones. We then investigate the polytope defined as their convex hull. We show that all the magog matrices are extreme and give a partial inequality description. Finally, we define another TSSCPP polytope as the convex hull of TSSCPP boolean triangles and determine its dimension, inequalities, vertices, and facets.
Source: Annals of Combinatorics
Authors: Vincent Holmlund, Jessica Striker
Institution: North Dakota State University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,790
OpenAlex ID: W4404480587