On Minimal-Perimeter Lattice Animals

Gill Barequet; Gil Ben-Shachar

doi:https://doi.org/10.1007/978-3-030-61792-9_41

On Minimal-Perimeter Lattice Animals

Gill Barequet, Gil Ben-Shachar

Computer Science

Technion - Israel Institute of Technology

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

Abstract

A lattice animal is a connected set of cells on a lattice. The perimeter of a lattice animal A consists of all the cells that do not belong to A, but that have a least one neighboring cell of A. We consider minimal-perimeter lattice animals, that is, animals whose periemeter is minimal for all animals of the same area, and provide a set of conditions that are sufficient for a lattice to have the property that inflating all minimal-perimeter animals of a certain size yields (without repetitions) all minimal-perimeter animals of a new, larger size. We demonstrate this result for polyhexes (animals on the two-dimensional hexagonal lattice).

Original language	English
Title of host publication	LATIN 2020
Subtitle of host publication	Theoretical Informatics - 14th Latin American Symposium 2021, Proceedings
Editors	Yoshiharu Kohayakawa, Flávio Keidi Miyazawa
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	519-531
Number of pages	13
ISBN (Print)	9783030617912
DOIs	https://doi.org/10.1007/978-3-030-61792-9_41
State	Published - 2020
Event	14th Latin American Symposium on Theoretical Informatics, LATIN 2020 - Sao Paulo, Brazil Duration: 5 Jan 2021 → 8 Jan 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12118 LNCS

Conference

Conference	14th Latin American Symposium on Theoretical Informatics, LATIN 2020
Country/Territory	Brazil
City	Sao Paulo
Period	5/01/21 → 8/01/21

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

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https://doi.org/10.1007/978-3-030-61792-9_41

Cite this

Barequet, G., & Ben-Shachar, G. (2020). On Minimal-Perimeter Lattice Animals. In Y. Kohayakawa, & F. K. Miyazawa (Eds.), LATIN 2020: Theoretical Informatics - 14th Latin American Symposium 2021, Proceedings (pp. 519-531). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12118 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-61792-9_41

Barequet, Gill ; Ben-Shachar, Gil. / On Minimal-Perimeter Lattice Animals. LATIN 2020: Theoretical Informatics - 14th Latin American Symposium 2021, Proceedings. editor / Yoshiharu Kohayakawa ; Flávio Keidi Miyazawa. Springer Science and Business Media Deutschland GmbH, 2020. pp. 519-531 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Barequet, G & Ben-Shachar, G 2020, On Minimal-Perimeter Lattice Animals. in Y Kohayakawa & FK Miyazawa (eds), LATIN 2020: Theoretical Informatics - 14th Latin American Symposium 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12118 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 519-531, 14th Latin American Symposium on Theoretical Informatics, LATIN 2020, Sao Paulo, Brazil, 5/01/21. https://doi.org/10.1007/978-3-030-61792-9_41

On Minimal-Perimeter Lattice Animals. / Barequet, Gill; Ben-Shachar, Gil.
LATIN 2020: Theoretical Informatics - 14th Latin American Symposium 2021, Proceedings. ed. / Yoshiharu Kohayakawa; Flávio Keidi Miyazawa. Springer Science and Business Media Deutschland GmbH, 2020. p. 519-531 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12118 LNCS).

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

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N2 - A lattice animal is a connected set of cells on a lattice. The perimeter of a lattice animal A consists of all the cells that do not belong to A, but that have a least one neighboring cell of A. We consider minimal-perimeter lattice animals, that is, animals whose periemeter is minimal for all animals of the same area, and provide a set of conditions that are sufficient for a lattice to have the property that inflating all minimal-perimeter animals of a certain size yields (without repetitions) all minimal-perimeter animals of a new, larger size. We demonstrate this result for polyhexes (animals on the two-dimensional hexagonal lattice).

AB - A lattice animal is a connected set of cells on a lattice. The perimeter of a lattice animal A consists of all the cells that do not belong to A, but that have a least one neighboring cell of A. We consider minimal-perimeter lattice animals, that is, animals whose periemeter is minimal for all animals of the same area, and provide a set of conditions that are sufficient for a lattice to have the property that inflating all minimal-perimeter animals of a certain size yields (without repetitions) all minimal-perimeter animals of a new, larger size. We demonstrate this result for polyhexes (animals on the two-dimensional hexagonal lattice).

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M3 - منشور من مؤتمر

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A2 - Kohayakawa, Yoshiharu

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Barequet G, Ben-Shachar G. On Minimal-Perimeter Lattice Animals. In Kohayakawa Y, Miyazawa FK, editors, LATIN 2020: Theoretical Informatics - 14th Latin American Symposium 2021, Proceedings. Springer Science and Business Media Deutschland GmbH. 2020. p. 519-531. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: https://doi.org/10.1007/978-3-030-61792-9_41

On Minimal-Perimeter Lattice Animals

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