Andrei Zelevinsky
Published 2005-07-13, updated 2006-05-13Version 4
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.
Comments: v2: 14 pages, 1 figure; historical account in the introduction modified, Section 5 reorganized, Corollary 5.2 supplied with a self-contained proof; v3: minor editorial changes, Proposition 7.2 supplied with a proof; v4: a few typos fixed, one reference updated, final version, to appear in Pure and Applied Mathematics Quarterly
Journal: Pure and Applied Mathematics Quarterly, 2 (2006), no. 3, 1-17
Polygon dissections and some generalizations of cluster complexes
A note on gamma triangles and local gamma vectors
P-graph Associahedra and Hypercube Graph Associahedra
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