Depth in arrangements: Dehn–Sommerville–Euler relations with applications-Reference-Cited by-同舟云学术

Depth in arrangements: Dehn–Sommerville–Euler relations with applications

Published:2024-05-03 Issue: Volume: Page:
ISSN:2367-1726
Container-title:Journal of Applied and Computational Topology
language:en
Short-container-title:J Appl. and Comput. Topology

Author:

Biswas Ranita^ORCID,Cultrera di Montesano Sebastiano^ORCID,Edelsbrunner Herbert^ORCID,Saghafian Morteza^ORCID

Abstract

AbstractThe depth of a cell in an arrangement of n (non-vertical) great-spheres in

$${\mathbb {S}}^d$$

S d is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn–Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements.

Funder

H2020 European Research Council

Austrian Science Fund

Institute of Science and Technology

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s41468-024-00173-w.pdf

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