dc.contributor.author
Barequet, Gill
dc.contributor.author
Rote, Günter
dc.contributor.author
Shalah, Mira
dc.date.accessioned
2018-06-08T04:08:02Z
dc.date.available
2014-04-03
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/16646
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-20827
dc.description.abstract
A polyomino (or animal) is an edge-connected set of squares on the regular
square lattice. Enumeration of polyominoes is an extremely hard problem in
enumerative combinatorics, with important applications in statistical physics.
We investigate one of the fundamental problems related to polyominoes, namely,
computing their asymptotic growth rate λ=lim A(n+1)/A(n) , where A(n) is the
number of polyominoes of size n. λ is also known as Klarner's constant. The
best lower and upper bounds on so far were roughly 3.98 and 4.65,
respectively, meaning that not even a single decimal digit of was known. Our
goal was to settle a long-standing problem: proving that λ>4. To this aim, we
developed a computer program which required extremely high computing resources
in terms of both running time and main memory. Our program showed rigorously
that λ>4.00253.
de
dc.rights.uri
http://www.cs.bgu.ac.il/~eurocg14/submission.html
dc.subject.ddc
000 Informatik, Informationswissenschaft, allgemeine Werke::000 Informatik, Wissen, Systeme::006 Spezielle Computerverfahren
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation
Abstracts of the 30th European Workshop on Computational Geometry (EuroCG'14),
Ein-Gedi, Israel, 3.-5. März 2014
dc.identifier.sepid
34205
dcterms.bibliographicCitation.url
http://www.cs.bgu.ac.il/~eurocg14/accepted.html
refubium.affiliation
Mathematik und Informatik
de
refubium.affiliation.other
Institut für Informatik
refubium.mycore.fudocsId
FUDOCS_document_000000020103
refubium.resourceType.isindependentpub
no
refubium.mycore.derivateId
FUDOCS_derivate_000000003395
dcterms.accessRights.openaire
open access
