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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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