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The area generating function for simple-2-column polyominoes with hexagonal cells


Feretić, Svjetlan; Trinajstić, Nenad
The area generating function for simple-2-column polyominoes with hexagonal cells // International Journal of Chemical Modeling, 3 (2010), 1-2; 115-129 (podatak o recenziji nije dostupan, članak, znanstveni)


Naslov
The area generating function for simple-2-column polyominoes with hexagonal cells

Autori
Feretić, Svjetlan ; Trinajstić, Nenad

Izvornik
International Journal of Chemical Modeling (1941-3955) 3 (2010), 1-2; 115-129

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Polyomino ; simple-2-column ; hexagonal cells ; area generating function ; q-series ; growth constant

Sažetak
Column-convex polygons were first counted by area several decades ago, and the result was found to be a simple, rational, generating function. In this chapter we generalize that result. Let a p-column polyomino be a polyomino whose columns can have 1, 2, ..., p connected components. Then column-convex polygons are equivalent to 1-convex polyominoes. The area generating function of even the simplest generalization, namely to 2-column polyominoes, is unlikely to be solvable. We therefore define a class of polyominoes which interpolates between column-convex polygons and 2-column polyominoes. We derive the area generating function of that class, using an extension of an existing algorithm. The growth constant of the new class is greater than the growth constant of column-convex polyominoes. A rather tight lower bound on the growth constant complements a compelling numerical analysis.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Kemija



POVEZANOST RADA


Projekt / tema
037-0000000-2779 - Diskretna matematika i primjene (Dragutin Svrtan, )
098-1770495-2919 - Razvoj metoda za modeliranje svojstava bioaktivnih molekula i proteina (Bono Lučić, )
177-0000000-0884 - Diskretni matematički modeli u kemiji (Damir Vukičević, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb,
Institut "Ruđer Bošković", Zagreb,
Građevinski fakultet, Rijeka,
Prirodoslovno-matematički fakultet, Split