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Bibliographic Details
Main Authors: Ivanov, Illya, Strachan, Cameron
Format: Preprint
Published: 2022
Subjects:
Online Access:https://arxiv.org/abs/2211.16621
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author Ivanov, Illya
Strachan, Cameron
author_facet Ivanov, Illya
Strachan, Cameron
contents Given a convex domain $C$, a $C$-polygon is an intersection of $n\geq 2$ homothets of $C$. If the homothets are translates of $C$ then we call the intersection a translative $C$-polygon. This paper proves that if $C$ is a strictly convex domain with $m$ singular boundary points, then the number of singular boundary points a $C$-polygon has is between $n$ and $2(n-1)+m$. For a translative $C$-polygon we show the number of singular boundary points is between $n$ and $n+m$.
format Preprint
id arxiv_https___arxiv_org_abs_2211_16621
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Vertex Classification of Planar C-polygons
Ivanov, Illya
Strachan, Cameron
Combinatorics
Geometric Topology
Given a convex domain $C$, a $C$-polygon is an intersection of $n\geq 2$ homothets of $C$. If the homothets are translates of $C$ then we call the intersection a translative $C$-polygon. This paper proves that if $C$ is a strictly convex domain with $m$ singular boundary points, then the number of singular boundary points a $C$-polygon has is between $n$ and $2(n-1)+m$. For a translative $C$-polygon we show the number of singular boundary points is between $n$ and $n+m$.
title Vertex Classification of Planar C-polygons
topic Combinatorics
Geometric Topology
url https://arxiv.org/abs/2211.16621