Open Access
| Issue |
RAIRO-Theor. Inf. Appl.
Volume 59, 2025
Generation, enumeration and tiling
|
|
|---|---|---|
| Article Number | 17 | |
| Number of page(s) | 16 | |
| DOI | https://doi.org/10.1051/ita/2025015 | |
| Published online | 19 November 2025 | |
- S.W. Golomb, Checker boards and polyominoes. Am. Math. Monthly 61 (1954) 675–682. [Google Scholar]
- M. Bousquet-Melou and R. Brak, Polygons, Polyominoes and Polycubes. Springer, Netherlands (2009) 43-78. [Google Scholar]
- A.R. Conway and A.J. Guttmann, On two-dimensional percolation. J. Phys. A: Math. Gen. 28 (1995) 891. [Google Scholar]
- X.G. Viennot, A survey of polyominoes enumeration, in 4th FPSAC Proceedings, Vol. 11. Publications du LACIM, Institut Mittag-Leffler (1992) 399-420. [Google Scholar]
- S.R. Broadbent and J.M. Hammersley, Percolation processes. I. Crystals and mazes. Math. Proc. Camb. Philos. Soc. 53 (1957) 629—-641. [Google Scholar]
- V. Hakim and J.P. Nadal, Exact results for 2D directed animals on a strip of finite width. J. Phys. A. Math. Gen. 16 (1983) 213–218. [Google Scholar]
- P.J. Peard and D.S. Gaunt, 1/d-expansions for the free energy of lattice animal models of a self-interacting branched polymer. J. Phys. A: Math. Gen. 28 (1995) 6109. [Google Scholar]
- V. Privman and N.M. Svrakic, Difference equations in statistical mechanics. I. Cluster statistics models. J. Stat. Phys. 51 (1988) 1091–1110. [Google Scholar]
- V. Privman and N.M. Svrakic, Directed Models of Polymers, Interfaces, and Clusters: Scaling and Finite-size Properties. Springer-Verlag, Berlin (1989). Lecture Notes in Physics 338. [Google Scholar]
- H.N.V. Temperley, Combinatorial problems suggested by the statistical mechanics of domains and of rubber-like molecules. Phys. Rev. 103 (1956) 1–16. [Google Scholar]
- G. Viennot, Problèmes combinatoires posés par la physique statistique. Astérisque 121–122 (1985) 225-246. [Google Scholar]
- D. Beauquier and M. Nivat, On translating one polyomino to tile the plane. Discrete Comput. Geom. 6 (1991) 575–592. [CrossRef] [MathSciNet] [Google Scholar]
- D. Beauquier, M. Nivat, É. Remila and M. Robson, Tiling figures of the plane with two bars. Comput. Geom. Theory Appl. 5 (1995) 1–25. [Google Scholar]
- R. Berger, The undecidability of the domino problem. Mem. Am. Math. Soc. 66 (1966) 72. [Google Scholar]
- J.W. Cannon, W.J. Floyd and W.R. Parry, Combinatorially regular polyomino tilings. Discrete Comput. Geom. 35 (2006) 269–285. [Google Scholar]
- B. Grünbaum and G.C. Shephard, Tilings and Patterns. W.H. Freeman and Company, New York (1989). [Google Scholar]
- D.A. Klarner, My life among the polyominoes. Nieuw Arch. Wiskunde. Derde Ser. 29 (1981) 156–177. [Google Scholar]
- T. Mansour, Smooth squared, triangular, and hexagonal bargraphs, Appl. Anal. Discrete Math. 18 (2024) 215–228. [Google Scholar]
- T. Mansour, Counting of descents in a bargraph and barpolyiamonds, J. Autom. Lang. Comb. 29 (2024) 41–48. [Google Scholar]
- E. Barcucci, A. Frosini and S. Rinaldi, Direct-convex polyominoes: ECO method and bijective results, in Proceedings of Formal Power Series and Algebraic Combinatorics 2002, edited by R. Brak, O. Foda, C. Greenhill, T. Guttman and A. Owczarek. Melbourne (2002). [Google Scholar]
- A. Conway, Enumerating 2D percolation series by the finite-lattice method: theory. J. Phys. A 28 (1995) 335–349. [Google Scholar]
- M. Delest and X.G. Viennot, Algebraic languages and polyominoes enumeration. Theoret. Comput. Sci. 34 (1984) 169–206. [Google Scholar]
- W.C. Yang and R.R. Meyer, Maximal and Minimal Polyiamonds. Technical report, University of Wisconsin-Madison (2002). [Google Scholar]
- G. Malen and É. Roldán, Polyiamonds attaining extremal topological properties. Part I. Available at https://arxiv.org/abs/1906.08447. [Google Scholar]
- M. Shalah, Formulae and Growth Rates of Animals on Cubical and Triangular Lattices. Ph.D. dissertation, Technion (2017). [Google Scholar]
- G. Barequet, M. Shalah and Y. Zheng, An improved lower bound on the growth constant of polyiamonds, in Proceedings of the 22nd International Computing and Combinatorics Conference (2017) 50-61 (appeared also in J. Combinator. Optim.). [Google Scholar]
- T. Mansour and R. Rastegar, Enumeration of various animals on triangular lattice. Eur. J. Combin. 394 (2021) 103294. [Google Scholar]
- T. Mansour, Smooth squared, triangular, and hexagonal bargraphs. Appl. Anal. Discrete Math. 18 (2024) 215–228. [Google Scholar]
- T. Mansour, Counting of descents in a bargraph and barpolyiamonds. J. Automata Languages Combin. 29 (2024) 41–48. [Google Scholar]
- T. Mansour and A.Sh. Shabani, Smooth column convex polyominoes. Discrete Comput. Geom. 68 (2022) 525–539. [Google Scholar]
- A. Knopfmacher and H. Prodinger, On Carlitz compositions. Eur. J. Combin. 19 (1998) 579–589. [Google Scholar]
- C. Banderier, M. Bousquet-Mélou, A. Denise, P. Flajolet, D. Gardy and D. GouyouBeauchamps, Generating functions for generating trees (Formal Power Series and Algebraic Combinatorics, Barcelona, 1999). Discrete Math. 246 (2002) 29–55. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.
