Research output: Working paper › Preprint
Research output: Working paper › Preprint
}
TY - UNPB
T1 - The two higher Stasheff-Tamari orders are equal
AU - Williams, Nicholas J.
N1 - 56 pages, A4, 1.3x line spacing, 10 figures; v2: added more environments for definitions, removed alternative proof
PY - 2021/6/2
Y1 - 2021/6/2
N2 - The set of triangulations of a cyclic polytope possesses two a priori different partial orders, known as the higher Stasheff-Tamari orders. The first of these orders was introduced by Kapranov and Voevodsky, while the second order was introduced by Edelman and Reiner, who also conjectured the two to coincide in 1996. In this paper we prove their conjecture, thereby substantially increasing our understanding of these orders. This result also has ramifications in the representation theory of algebras, as established in previous work of the author. Indeed, it means that the two corresponding orders on tilting modules, cluster-tilting objects and their maximal chains are equal for the higher Auslander algebras of type $A$.
AB - The set of triangulations of a cyclic polytope possesses two a priori different partial orders, known as the higher Stasheff-Tamari orders. The first of these orders was introduced by Kapranov and Voevodsky, while the second order was introduced by Edelman and Reiner, who also conjectured the two to coincide in 1996. In this paper we prove their conjecture, thereby substantially increasing our understanding of these orders. This result also has ramifications in the representation theory of algebras, as established in previous work of the author. Indeed, it means that the two corresponding orders on tilting modules, cluster-tilting objects and their maximal chains are equal for the higher Auslander algebras of type $A$.
KW - math.CO
KW - math.RT
KW - 52B05, 05B45, 06A07, 52B12, 05E10
M3 - Preprint
BT - The two higher Stasheff-Tamari orders are equal
PB - EMS Press
ER -