Counting Polyominoes on Twisted Cylinders
We improve the lower bounds on Klarner's constant, which describes the exponential growth rate of the number of polyominoes (connected subsets of grid squares) with a given number of squares. We achieve this by analyzing polyominoes on a different surface, a so-called $\textit{twisted cylinder}...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2005-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3446/pdf |
| _version_ | 1797270327127965696 |
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| author | Gill Barequet Micha Moffie Ares Ribó Günter Rote |
| author_facet | Gill Barequet Micha Moffie Ares Ribó Günter Rote |
| author_sort | Gill Barequet |
| collection | DOAJ |
| description | We improve the lower bounds on Klarner's constant, which describes the exponential growth rate of the number of polyominoes (connected subsets of grid squares) with a given number of squares. We achieve this by analyzing polyominoes on a different surface, a so-called $\textit{twisted cylinder}$ by the transfer matrix method. A bijective representation of the "states'' of partial solutions is crucial for allowing a compact representation of the successive iteration vectors for the transfer matrix method. |
| first_indexed | 2024-04-25T02:02:30Z |
| format | Article |
| id | doaj.art-0f672749826c45478e0b102ea8875822 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:02:30Z |
| publishDate | 2005-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-0f672749826c45478e0b102ea88758222024-03-07T14:41:15ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502005-01-01DMTCS Proceedings vol. AE,...Proceedings10.46298/dmtcs.34463446Counting Polyominoes on Twisted CylindersGill Barequet0Micha Moffie1Ares Ribó2Günter Rote3https://orcid.org/0000-0002-0351-5945Department of Computer Science [Haifa]Department of Computer Science [Haifa]Institut für Informatik [Berlin]Institut für Informatik [Berlin]We improve the lower bounds on Klarner's constant, which describes the exponential growth rate of the number of polyominoes (connected subsets of grid squares) with a given number of squares. We achieve this by analyzing polyominoes on a different surface, a so-called $\textit{twisted cylinder}$ by the transfer matrix method. A bijective representation of the "states'' of partial solutions is crucial for allowing a compact representation of the successive iteration vectors for the transfer matrix method.https://dmtcs.episciences.org/3446/pdfpolyominocombinatorial counting[info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co] |
| spellingShingle | Gill Barequet Micha Moffie Ares Ribó Günter Rote Counting Polyominoes on Twisted Cylinders Discrete Mathematics & Theoretical Computer Science polyomino combinatorial counting [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| title | Counting Polyominoes on Twisted Cylinders |
| title_full | Counting Polyominoes on Twisted Cylinders |
| title_fullStr | Counting Polyominoes on Twisted Cylinders |
| title_full_unstemmed | Counting Polyominoes on Twisted Cylinders |
| title_short | Counting Polyominoes on Twisted Cylinders |
| title_sort | counting polyominoes on twisted cylinders |
| topic | polyomino combinatorial counting [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/3446/pdf |
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