Nested complexes and their polyhedral realizations

Details Nested complexes and their polyhedral realizations Nested complexes and their polyhedral realizations

2005-07-13

arxiv.org/abs/math/0507277v4

Pure and Applied Mathematics Quarterly, 2 (2006), no. 3, 1-17

Mathematics

Combinatorics

v2: 14 pages, 1 figure; historical account in the introduction modified, Section 5 reorganized, Corollary 5.2 supplied with a

Scientific paper

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.

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