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Pregled bibliografske jedinice broj: 570673

Časopis

Autori: Feretić, Svjetlan
Naslov: Polyominoes with nearly convex columns : A semi-directed model
( Polyominoes with nearly convex columns : A semi-directed model )
Izvornik: ARS Mathematica Contemporanea (1855-3966) 5 (2012), 1; 107-126
Vrsta rada: članak
Ključne riječi: polyomino; hexagonal-celled; nearly convex column; semi-directed; area generating function
( polyomino; hexagonal-celled; nearly convex column; semi-directed; area generating function )
Sažetak:
Column-convex polyominoes are by now a well- explored model. So far, however, no attention has been given to polyominoes whose columns can have either one or two connected components. This little known kind of polyominoes seems not to be manageable as a whole. To obtain solvable models, one needs to introduce some restrictions. This paper is focused on polyominoes with hexagonal cells. The restrictions just mentioned are semi- directedness and an upper bound (say m) on the size of the gap within a column. As the upper bound m grows, the solution of the model tends to break into more and more cases. We computed the area generating functions for m = 1, m = 2 and m = 3. In this paper, the m = 1 and m = 2 models are solved in full detail. To keep the size of the paper within reasonable limits, the result for the m = 3 model is stated without proof. The m = 1, m = 2 and m = 3 models have rational area generating functions, as column-convex polyominoes do. (It is practically sure, although we leave it unproved, that the area generating functions are also rational for m = 4, m = 5, ...) However, the growth constants of the new models are 4.114908 and more, whereas the growth constant of column- convex polyominoes is 3.863131.
Projekt / tema: 177-0000000-0884, 037-0000000-2779
Izvorni jezik: eng
Rad je indeksiran u
bazama podataka:
Current Contents Connect (CCC)
Scopus
SCI-EXP, SSCI i/ili A&HCI
Science Citation Index Expanded (SCI-EXP) (sastavni dio Web of Science Core Collectiona)
Kategorija: Znanstveni
Znanstvena područja:
Matematika
Puni text rada: 570673.amc_2012_objavljeno.pdf (tekst priložen 10. Vel. 2012. u 13:13 sati)
URL Internet adrese: http://amc.imfm.si/index.php/amc/article/view/162/156
http://amc.imfm.si/index.php/amc
URL cjelovitog teksta:
Google Scholar: Polyominoes with nearly convex columns : A semi-directed model
Upisao u CROSBI: svjetlan.feretic@gradri.hr (svjetlan.feretic@gradri.hr), 10. Vel. 2012. u 13:13 sati



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