An improved lower bound on the growth constant of polyiamonds

Gill Barequet; Mira Shalah; Yufei Zheng

doi:10.1007/978-3-319-62389-4_5

An improved lower bound on the growth constant of polyiamonds

Gill Barequet, Mira Shalah, Yufei Zheng

Computer Science

Technion - Israel Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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 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.

Original language	English
Title of host publication	Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings
Editors	Yixin Cao, Jianer Chen
Pages	50-61
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-319-62389-4_5
State	Published - 2017
Event	23rd International Conference on Computing and Combinatorics, COCOON 2017 - Hong Kong, China Duration: 3 Aug 2017 → 5 Aug 2017

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10392 LNCS

Conference

Conference	23rd International Conference on Computing and Combinatorics, COCOON 2017
Country/Territory	China
City	Hong Kong
Period	3/08/17 → 5/08/17

Keywords

Growth constant
Lattice animals
Polyiamonds

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-62389-4_5

Cite this

Barequet, G., Shalah, M., & Zheng, Y. (2017). An improved lower bound on the growth constant of polyiamonds. In Y. Cao, & J. Chen (Eds.), Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings (pp. 50-61). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10392 LNCS). https://doi.org/10.1007/978-3-319-62389-4_5

Barequet, Gill ; Shalah, Mira ; Zheng, Yufei. / An improved lower bound on the growth constant of polyiamonds. Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings. editor / Yixin Cao ; Jianer Chen. 2017. pp. 50-61 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "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 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.",

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Barequet, G, Shalah, M & Zheng, Y 2017, An improved lower bound on the growth constant of polyiamonds. in Y Cao & J Chen (eds), Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10392 LNCS, pp. 50-61, 23rd International Conference on Computing and Combinatorics, COCOON 2017, Hong Kong, China, 3/08/17. https://doi.org/10.1007/978-3-319-62389-4_5

An improved lower bound on the growth constant of polyiamonds. / Barequet, Gill; Shalah, Mira; Zheng, Yufei.
Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings. ed. / Yixin Cao; Jianer Chen. 2017. p. 50-61 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10392 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Barequet G, Shalah M, Zheng Y. An improved lower bound on the growth constant of polyiamonds. In Cao Y, Chen J, editors, Computing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings. 2017. p. 50-61. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-62389-4_5

An improved lower bound on the growth constant of polyiamonds

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Keywords

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