NDLI: Permutonestohedra

Content Provider	Springer Nature Link
Author	Gaiffi, Giovanni
Copyright Year	2014
Abstract	There are several real spherical models associated with a root arrangement, depending on the choice of a building set. The connected components of these models are manifolds with corners which can be glued together to obtain the corresponding real De Concini–Procesi models. In this paper, starting from any root system $$\Phi $$ with finite Coxeter group $$W$$ and any $$W$$ -invariant building set, we describe an explicit realization of the real spherical model as a union of polytopes (nestohedra) that lie inside the chambers of the arrangement. The main point of this realization is that the convex hull of these nestohedra is a larger polytope, a permutonestohedron, equipped with an action of $$W$$ or also, depending on the building set, of $$Aut(\Phi )$$ . The permutonestohedra are natural generalizations of Kapranov’s permutoassociahedra.
Starting Page	125
Ending Page	155
Page Count	31
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	41
Issue Number	1
e-ISSN	15729192
Language	English
Publisher	Springer US
Publisher Date	2014-05-22
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Models of arrangements Coxeter groups Nestohedra Combinatorics Convex and Discrete Geometry Order, Lattices, Ordered Algebraic Structures Computer Science Group Theory and Generalizations
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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