Nested complexes and their polyhedral realizations
By Andrei Zelevinsky. 2005
81 citations recorded by the source corpus.
This note which can be viewed as a complement to Alex Postnikov's paper math.CO/0507163, presents a self-contained overview of basic properties of nested complexes and their two dual polyhedral realizations: as complete simplicial fans, and as simple polytopes. Most of the results are not new; our aim is to bring into focus a striking similarity between nested complexes and associated fans and polytopes on one side, and cluster complexes and generalized associahedra introduced and studied in hep-th/0111053, math.CO/0202004, on the other side.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/c9b542e8a0602daf66a80a7a4a400c93e8ecde08
How researchers see this paper
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In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
- Alexander Postnikov
- Lauren K. Williams
- David E. Speyer
- Thomas Lam
- Federico Ardila
- Dan Xie
- Greg Muller
- Yuji Kodama
In Geometry and Topology
- Alexander Postnikov
- Lauren K. Williams
- David E. Speyer
- Thomas Lam
- Dan Xie
- Greg Muller
- Federico Ardila
- Yuji Kodama
Citations in the corpus
- Gamma-positivity in combinatorics and geometry (2017, unknown): “We begin with a few definitions, following [134].”
- Permutohedra, Associahedra, and Beyond (2005, background): “In [42], Zelevinsky gives an alternative construction for generalized permutohedra associated with building sets, which is parallel to the construction from [7].”