Napredna pretraga

## Polyominoes with nearly convex columns: An undirected model

Feretić, Svjetlan; Guttmann, Anthony J.
Polyominoes with nearly convex columns: An undirected model // Glasnik matematički, 45 (2010), 2; 325-346 doi:10.3336/gm (međunarodna recenzija, članak, znanstveni)

Naslov
Polyominoes with nearly convex columns: An undirected model

Autori
Feretić, Svjetlan ; Guttmann, Anthony J.

Izvornik
Glasnik matematički (0017-095X) 45 (2010), 2; 325-346

Ključne riječi
Polyomino; hexagonal cell; nearly convex column; area generating function; growth constant

Sažetak
Column-convex polyominoes were introduced in 1950's by Temperley, a mathematical physicist working on ``lattice gases''. By now, column-convex polyominoes are a popular and well-understood model. There exist several generalizations of column-convex polyominoes. However, the enumeration by area has been done for only one of the said generalizations, namely for multi-directed animals. In this paper, we introduce a new sequence of supersets of column-convex polyominoes. Our model (we call it level m column-subconvex polyominoes) is defined in a simple way: every column has at most two connected components and, if there are two connected components, the gap between them consists of at most m cells. We focus on the case when cells are hexagons and we compute the area generating functions for the levels one and two. Both of those generating functions are q-series, whereas the area generating function of column-convex polyominoes is a rational function. The growth constants of level one and level two column-subconvex polyominoes are 4.319139 and 4.509480, respectively. For comparison, the growth constants of column-convex polyominoes, multi-directed animals and all polyominoes are 3.863131, 4.587894 and 5.183148, respectively.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
037-0000000-2779 - Diskretna matematika i primjene (Dragutin Svrtan, )
177-0000000-0884 - Diskretni matematički modeli u kemiji (Damir Vukičević, )

Ustanove
Građevinski fakultet, Rijeka

Autor s matičnim brojem:
Svjetlan Feretić, (137471)

#### Časopis indeksira:

• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus

#### Uključenost u ostale bibliografske baze podataka:

• INSPEC
• MathSciNet
• Zentrallblatt für Mathematik/Mathematical Abstracts
• Mathematical Reviews
• Referativni Žurnal - Matematika
• Scopus
• Current Mathematical Publications
• Science Citation Index Expanded
• Reference List Journals of MathSciNet