Triangulations of Cyclic Polytopes and higher Bruhat Orders
| dc.contributor.author | Rambau, Jörg | |
| dc.date.accessioned | 2021-12-17T10:07:01Z | |
| dc.date.available | 2021-12-17T10:07:01Z | |
| dc.date.issued | 1996 | |
| dc.description.abstract | Recently Edelman & Reiner} suggested two poset structures S}1(n,d) and S}2(n,d) on the set of all triangulations of the cyclic d-polytope C(n,d) with n vertices. Both posets are generalizations of the well-studied Tamari lattice. While S}2(n,d) is bounded by definition, the same is not obvious for S}1(n,d). In the paper by Edelman & Reiner} the bounds of S}2(n,d) were also confirmed for S}1(n,d) whenever d \le 5, leaving the general case as a conjecture. In this paper their conjecture is answered in the affirmative for all~d, using several new functorial constructions. Moreover, a structure theorem is presented, stating that the elements of S}1(n,d+1) are in one-to-one correspondence to certain equivalence classes of maximal chains in S}1(n,d). In order to clarify the connection between S}1(n,d) and the higher Bruhat order B}(n-2,d-1) of Manin & Schechtman}, we define an order-preserving map from B}(n-2,d-1) to S}1(n,d), thereby concretizing a result by Kapranov & Voevodsky} in the theory of ordered n-categories. | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15594 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14367 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | bruhat order | en |
| dc.subject.other | cyclic polytopes | en |
| dc.subject.other | edelman reiner | en |
| dc.subject.other | several new functorial construction | en |
| dc.subject.other | maximal chain | en |
| dc.subject.other | similar method | en |
| dc.subject.other | structure theorem | en |
| dc.subject.other | well-studied tamari lattice | en |
| dc.subject.other | kapranov voevod-sky | en |
| dc.subject.other | general case | en |
| dc.subject.other | order-preserving map | en |
| dc.subject.other | one-to-one correspondence | en |
| dc.subject.other | manin schechtman | en |
| dc.subject.other | ordered n-categories | en |
| dc.subject.other | certain equivalence class | en |
| dc.subject.other | poset structure | en |
| dc.subject.other | cyclic d-polytope | en |
| dc.title | Triangulations of Cyclic Polytopes and higher Bruhat Orders | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 1996, 496 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
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