Totally symmetric self-complementary plane partition matrices and related polytopes
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913583697231872 |
|---|---|
| author | Holmlund, Vincent Striker, Jessica |
| author_facet | Holmlund, Vincent Striker, Jessica |
| contents | Plane partitions in the totally symmetric self-complementary symmetry class (TSSCPP) are known to be equinumerous with n x 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}-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03564 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Totally symmetric self-complementary plane partition matrices and related polytopes Holmlund, Vincent Striker, Jessica Combinatorics 05A05, 52B05 Plane partitions in the totally symmetric self-complementary symmetry class (TSSCPP) are known to be equinumerous with n x 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}-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. |
| title | Totally symmetric self-complementary plane partition matrices and related polytopes |
| topic | Combinatorics 05A05, 52B05 |
| url | https://arxiv.org/abs/2312.03564 |