Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 49, No. 1, pp. 125136 (2008) 

Convex hulls of polyominoesSascha KurzBusiness Mathematics, University of Bayreuth, D95440 Bayreuth, Germany, email: sascha.kurz@unibayreuth.deAbstract: In this article we prove a conjecture of Bezdek, Braß, and Harborth concerning the maximum volume of the convex hull of any facettofacet connected system of $n$ unit hypercubes in $\mathbb{R}^d$ [B]. For $d=2$ we enumerate the extremal polyominoes and determine the set of possible areas of the convex hull for each $n$. [B] Bezdek, K.; Braß, P.; Harborth, H.: Maximum convex hulls of connected systems of segments and of polyominoes. Beitr. Algebra Geom. {\bf 35}(1) (1994), 3743. Festschrift on the occasion of the 65th birthday of Otto Krötenheerdt. Keywords: polyominoes, convex hull, didotype problem, isoperimetric inequality Classification (MSC2000): 05B50$^\star$, 05D99, 52C99 Full text of the article:
Electronic version published on: 26 Feb 2008. This page was last modified: 28 Jan 2013.
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