An Improved Lower Bound on the Growth Constant of Polyiamonds
| Autor: | Yufei Zheng, Mira Shalah, Gill Barequet |
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| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Concatenation 0102 computer and information sciences 02 engineering and technology Extension (predicate logic) 01 natural sciences Upper and lower bounds Set (abstract data type) 010201 computation theory & mathematics 020204 information systems Theory of computation 0202 electrical engineering electronic engineering information engineering Polyiamond Hexagonal lattice Constant (mathematics) Mathematics |
| Zdroj: | Lecture Notes in Computer Science ISBN: 9783319623887 COCOON |
| DOI: | 10.1007/978-3-319-62389-4_5 |
| Popis: | A polyiamond is an edge-connected set of cells on the triangular lattice. In this paper we provide an improved lower bound on the asymptotic growth constant of polyiamonds, proving that it is at least 2.8424. The proof of the new bound is based on a concatenation argument and on elementary calculus. We also suggest a nontrivial extension of this method for improving the bound further. However, the proposed extension is based on an unproven (yet very reasonable) assumption. |
| Databáze: | OpenAIRE |
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