Tetromino tilings on the Tetris board* * The first author (corresponding author) was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2022R1F1A1064273).

Seungsang Oh; Jaehwan Yi

doi:10.1088/1402-4896/acdc61

Tetromino tilings on the Tetris board* * The first author (corresponding author) was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2022R1F1A1064273).

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Abstract

Tetrominos, comprised of four identical squares joined together along edges, have achieved substantial popular recognition as the elemental components of the widely known game, Tetris. In this paper, we present a recursive formula aimed at exact enumeration of tetromino tilings on a rectangular board with dimensions m × n. Furthermore, we modify the tiling criterion to mirror the Tetris gameplay, resulting in what we term Tetris tiling of height n. By employing this adjusted condition, we accurately calculate the total number of Tetris tilings. Additionally, the asymptotic behavior of the growth rate associated with the tetromino tiling is discussed.

Original language	English
Article number	075228
Journal	Physica Scripta
Volume	98
Issue number	7
DOIs	https://doi.org/10.1088/1402-4896/acdc61
Publication status	Published - 2023 Jul 1

Bibliographical note

Publisher Copyright:
© 2023 IOP Publishing Ltd.

Keywords

enumeration
tetris
tetromino
tiling

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics
Mathematical Physics
Condensed Matter Physics

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abstract = "Tetrominos, comprised of four identical squares joined together along edges, have achieved substantial popular recognition as the elemental components of the widely known game, Tetris. In this paper, we present a recursive formula aimed at exact enumeration of tetromino tilings on a rectangular board with dimensions m × n. Furthermore, we modify the tiling criterion to mirror the Tetris gameplay, resulting in what we term Tetris tiling of height n. By employing this adjusted condition, we accurately calculate the total number of Tetris tilings. Additionally, the asymptotic behavior of the growth rate associated with the tetromino tiling is discussed.",

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N2 - Tetrominos, comprised of four identical squares joined together along edges, have achieved substantial popular recognition as the elemental components of the widely known game, Tetris. In this paper, we present a recursive formula aimed at exact enumeration of tetromino tilings on a rectangular board with dimensions m × n. Furthermore, we modify the tiling criterion to mirror the Tetris gameplay, resulting in what we term Tetris tiling of height n. By employing this adjusted condition, we accurately calculate the total number of Tetris tilings. Additionally, the asymptotic behavior of the growth rate associated with the tetromino tiling is discussed.

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Tetromino tilings on the Tetris board* * The first author (corresponding author) was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2022R1F1A1064273).

Abstract

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Keywords

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