The University of Arizona

Events & News

Colloquium

CategoryLecture
DateThursday, January 10, 2013
Time11:00 am
Concludes12:00 pm
LocationGould-Simpson 906
SpeakerTorsten Ueckerdt
AffiliationKarlshure Institute of Technology, Germany

Clumsy Packings with Polyominoes

We are interested in packings with polyominoes from a fixed set called the palette. Packings are inclusion-maximal sets of disjoint polyominoes in the plane, each being a translated copy from the palette. A packing with smallest density, i.e., one that leaves the most uncovered area, is called a clumsy packing. We show that for some palettes all clumsy packings are aperiodic, while for every palette and every positive epsilon there is a periodic packing which is epsilon-close to being clumsy. Furthermore we show that the question whether a clumsy packing for a given palette has density at most some rational number d is undecidable. Finally we investigate the polyomino of size k that gives the "clumsiest" packing among all polynomioes of size k.