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Abstract: We investigate several hyperplane arrangements that can be viewed as deformations of Coxeter arrangements. In particular, we prove a conjecture of Linial and Stanley that the number of regions of the arrangement x i x j = 1; 1 i < j n; is equal to the number of alternating trees on n+ 1 vertices. Remarkably, these numbers have several additional combinatorial interpretations in terms of binary trees, partially ordered sets, and tournaments. More generally, we give formulae for the number... (Update)
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...9840383. The second author was supported by NSF grant #DMS 9500714. A version of 14 April 1997 of this paper is available as E print [21]. The current version contains two additional sections on weighted trees and asymptotics. One special case of such deformations is the...
...For g 0 it is the classical Coxeter or reflection arrangement of type An . The case g 1 has been studied by Postnikov and Stanley [22]. The expansion cone of a 1d point set is the positive cell in the arrangement An , and our associahedron is a bounded face of the polyhedron...
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BibTeX entry: (Update)
A. Postnikov and R. Stanley, Deformations of Coxeter hyperplane arrangements, Preprint dated April 14, 1997. http://citeseer.ist.psu.edu/postnikov00deformations.html More
@misc{ postnikov97deformations,
author = "A. Postnikov and R. Stanley",
title = "Deformations of Coxeter hyperplane arrangements",
text = "A. Postnikov and R. Stanley, Deformations of Coxeter hyperplane arrangements,
Preprint dated April 14, 1997.",
year = "1997",
url = "citeseer.ist.psu.edu/postnikov00deformations.html" }
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