Treffer: On the number of hexagonal polyominoes

Title:
On the number of hexagonal polyominoes
Authors:
VÖGE, Markus, GUTTMANN, Anthony J
Source:
Random generation of combinatorial objects and bijective combinatoricsTheoretical computer science. 307(2):433-453
Publisher Information:
Amsterdam: Elsevier, 2003.
Publication Year:
2003
Physical Description:
print, 28 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Problèmes combinatoires classiques, Classical combinatorial problems, Algèbre matricielle, Matrix algebra, Combinatoire, Combinatorics, Combinatoria, Correction, Corrections, Corrección, Enumération, Enumeration, Enumeración, Exposant critique, Critical exponent, Exponente crítico, Fonction génératrice, Generating function, Función generatriz, Méthode, Method, Método, Nombre, Number, Número, Ordinateur, Computer, Computadora, Plan, Plane, Plano, Taille, Size, Talla, Transfert, Transfer, Transferencia, Treillis, Lattice, Enrejado, Polyomino, Treillis hexagonal, Hexagonal lattice
Document Type:
Konferenz Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia
ISSN:
0304-3975
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=15176393
Rights:
Copyright 2004 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.15176393
Database:
PASCAL Archive

Weitere Informationen

A combination of the refined finite lattice method and transfer matrices allows a radical increase in the computer enumeration of polyominoes on the hexagonal lattice (equivalently, site clusters on the triangular lattice), pn with n hexagons. We obtain pn for n < 35. We prove that pn = τn+o(n), obtain the bounds 4.8049 ≤ τ ≤ 5.9047, and estimate that τ=5.1831478(17). Finally, we provide compelling numerical evidence that the generating function Σ pnzn A(z)log(1-τz), for z → (1/τ)- with A(z) holomorphic in a cut plane, estimate A(1/τ) and predict the sub-leading asymptotic behaviour, identifying a non-analytic correction-to-scaling term with exponent Δ=3/2. On the basis of universality and previous numerical work we argue that the mean-square radius of gyration <R2g>n of polyominoes of size n grows as n2v, with v = 0.64115(5).