Details
| Original language | English |
|---|---|
| Title of host publication | Combinatorial Structures in Algebra and Geometry |
| Subtitle of host publication | NSA 26, Constanța, Romania, August 26–September 1, 2018 |
| Editors | Dumitru I. Stamate, Tomasz Szemberg |
| Place of Publication | Cham |
| Publisher | Springer Nature Switzerland AG |
| Pages | 95-114 |
| Number of pages | 20 |
| Volume | 331 |
| ISBN (electronic) | 978-3-030-52111-0 |
| ISBN (print) | 978-3-030-52110-3 |
| Publication status | Published - 2 Sept 2020 |
| Event | 26th National School on Algebra, NSA 2018 - Constanta, Romania Duration: 26 Aug 2018 → 1 Sept 2018 |
Publication series
| Name | Springer Proceedings in Mathematics and Statistics |
|---|---|
| Volume | 331 |
| ISSN (Print) | 2194-1009 |
| ISSN (electronic) | 2194-1017 |
Abstract
Stanley (1986) introduced the order polytope and chain polytope of a partially ordered set and showed that they are related by a piecewise-linear homeomorphism. In this paper we view order and chain polytopes as instances of distributive and anti-blocking polytopes, respectively. Both these classes of polytopes are defined in terms of the componentwise partial order on. We generalize Stanley’s PL-homeomorphism to a large class of distributive polyhedra using infinite walks in marked networks.
Keywords
- Anti-blocking polyhedra, Chain polytopes, Distributive polyhedra, Marked networks, Order polytopes, Piecewise-linear maps
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
Cite this
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Combinatorial Structures in Algebra and Geometry: NSA 26, Constanța, Romania, August 26–September 1, 2018. ed. / Dumitru I. Stamate; Tomasz Szemberg. Vol. 331 Cham: Springer Nature Switzerland AG, 2020. p. 95-114 (Springer Proceedings in Mathematics and Statistics; Vol. 331).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - On Piecewise-Linear Homeomorphisms Between Distributive and Anti-blocking Polyhedra
AU - Pegel, Christoph
AU - Sanyal, Raman
N1 - Publisher Copyright: © 2020, Springer Nature Switzerland AG.
PY - 2020/9/2
Y1 - 2020/9/2
N2 - Stanley (1986) introduced the order polytope and chain polytope of a partially ordered set and showed that they are related by a piecewise-linear homeomorphism. In this paper we view order and chain polytopes as instances of distributive and anti-blocking polytopes, respectively. Both these classes of polytopes are defined in terms of the componentwise partial order on. We generalize Stanley’s PL-homeomorphism to a large class of distributive polyhedra using infinite walks in marked networks.
AB - Stanley (1986) introduced the order polytope and chain polytope of a partially ordered set and showed that they are related by a piecewise-linear homeomorphism. In this paper we view order and chain polytopes as instances of distributive and anti-blocking polytopes, respectively. Both these classes of polytopes are defined in terms of the componentwise partial order on. We generalize Stanley’s PL-homeomorphism to a large class of distributive polyhedra using infinite walks in marked networks.
KW - Anti-blocking polyhedra
KW - Chain polytopes
KW - Distributive polyhedra
KW - Marked networks
KW - Order polytopes
KW - Piecewise-linear maps
UR - http://www.scopus.com/inward/record.url?scp=85091343326&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1911.12090
DO - 10.48550/arXiv.1911.12090
M3 - Conference contribution
SN - 978-3-030-52110-3
VL - 331
T3 - Springer Proceedings in Mathematics and Statistics
SP - 95
EP - 114
BT - Combinatorial Structures in Algebra and Geometry
A2 - Stamate, Dumitru I.
A2 - Szemberg, Tomasz
PB - Springer Nature Switzerland AG
CY - Cham
T2 - 26th National School on Algebra, NSA 2018
Y2 - 26 August 2018 through 1 September 2018
ER -