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Convex hulls of polyominoes

URN to cite this document: urn:nbn:de:bvb:703-opus4-2456

Title data

Kurz, Sascha:
Convex hulls of polyominoes.
Bayreuth , 2007

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Abstract

In this article we prove a conjecture of Bezdek, Brass, and Harborth concerning the maximum volume of the convex hull of any facet-to-facet connected system of $n$ unit hypercubes in $mathbb{R}^d$. For $d=2$ we enumerate the extremal polyominoes and determine the set of possible areas of the convex hull for each $n$.

Abstract in another language

Wir beweisen eine Vermutung von Bezdek, Brass und Harborth über das maximale Volumen der konvexen Hülle von Seite-an-Seite gelagerten d-dimensionalen Einheitshyperwürfeln. Für d=2 enumerieren wir die extremalen Konfigurationen und bestimmen die möglichen Flächeninhalte der konvexen Hülle aus n Einheitsquadraten.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): Source: erscheint in "Beiträge zur Algebra und Geometrie"
Keywords: Polyomino; Diskrete Geometrie; Konvexe Hülle
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy > Chair Mathematics in Economy - Univ.-Prof. Dr. Jörg Rambau
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-opus4-2456
Date Deposited: 25 Apr 2014 12:19
Last Modified: 27 Mar 2019 13:01
URI: https://epub.uni-bayreuth.de/id/eprint/735

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