Number of Spinal-Convex Polyominoes
DOI:
https://doi.org/10.31642/JoKMC/2018/060303Abstract
In his paper we describe a restricted class of polyominoes called spinal-convex polyominoes. Spinal-convex polyominoes created by two columns such that column 1 (respectively, column2) with at most two set columns sequence of adjacent ominoes and column 2 (respectively, column1) with at least one set column sequence of adjacent ominoes. In addition, this study reveals new combinatorial method of enumerating spinal-convex polyominoes. Keywords—: Polyominoes, Spinal-convex, Set column sequence, enumerating.Downloads
References
Golomb, S. W. , Checker boards and polyominoes. The American Mathematical Monthly, 1954 Vol. 61, No.10, PP.675-682. DOI: https://doi.org/10.1080/00029890.1954.11988548
Klarner, D. A. , Enumeration involving sums over compositions. Ph.D Thesis. University of Alberta, 1966.
Rechnitzer, Andrew . Some problems in the counting of lattice animals, polyominoes, polygons and walks.,Ph.D Thesis. University of Melbourne, 2001.
David A. Klarner. Cell growth problems. Canadian Journal of Mathematics, 1967, Vol.19, PP. 851-863. DOI: https://doi.org/10.4153/CJM-1967-080-4
Bender, Edward. Convex n-ominoes. Discrete Mathematics, 1974, Vol. 8, P.P. 219-226. DOI: https://doi.org/10.1016/0012-365X(74)90134-4
Barcucci, El and Bertoli, F and Del Lungo, A and Pinzani, R. The average height of directed column-convex polyominoes having square, hexagonal and triangular cells. Mathematical and Computer Modelling, 1997, Vol.26, No.(8-10),PP. 27-36. DOI: https://doi.org/10.1016/S0895-7177(97)00197-0
Del Lungo, Alberto. Polyominoes defined by two vectors. Theoretical Computer Science, 1994, Vol. 127, No. 1, PP. 187-198. DOI: https://doi.org/10.1016/0304-3975(94)90107-4
Guttmann, AJ and Enting, IG,. The number of convex polygons on the square and honeycomb lattices. Journal of Physics A: Mathematical and General, 1988, Vol. 21, No. 8,PP. 467-474. DOI: https://doi.org/10.1088/0305-4470/21/8/007
Woeginger, Gerhard. The reconstruction of polyominoes from their orthogonal projections. Information Processing Letters, 2001, Vol. 77, P.P. 225-229. DOI: https://doi.org/10.1016/S0020-0190(00)00162-9
Battaglino, Daniela. Enumeration of polyominoes defined in terms of pattern avoidance or convexity constraints. Ph.D. Thesis, University of Siena and the University of Nice Sophia, 2014.
Castiglione, Giusi and Frosini, Andrea and Restivo, Antonio and Rinaldi, Simone. Enumeration of L-convex polyominoes by rows and columns. Theoretical Computer Science, 2005, Vol. 347, No. (1-2), P.P. 336-352. DOI: https://doi.org/10.1016/j.tcs.2005.06.031
Castiglione, Giusi, and Antonio Restivo. Reconstruction of L-convex Polyominoes. Electronic Notes in Discrete Mathematics, 2003, Vol. 12, P.P. 290-301. DOI: https://doi.org/10.1016/S1571-0653(04)00494-9
Enrica Duchi, Simone Rinaldi, and Gilles Schaeffer. The number of Z-convex polyominoes. Advances in applied mathematics, 2008, Vol. 40, No.1, P.P. 54-72. DOI: https://doi.org/10.1016/j.aam.2006.07.004
Mohommed, E. F., Ibrahim, H. & Ahmad, N. Enumeration of n-connected objects inscribed in an abacus.} Journal of Algebra, Number Theory & Applications. 2017, Vol. 39 : 843-874. DOI: https://doi.org/10.17654/NT039060843
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 Mustafa A. Sabri, Eman F. Mohomme
This work is licensed under a Creative Commons Attribution 4.0 International License.
which allows users to copy, create extracts, abstracts, and new works from the Article, alter and revise the Article, and make commercial use of the Article (including reuse and/or resale of the Article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made and the licensor is not represented as endorsing the use made of the work.
