Enumerating Polyominoes with Fixed Perimeter Defect

Andrei Asinowski; Gill Barequet; Yufei Zheng

doi:https://doi.org/10.1016/j.endm.2017.06.021

Enumerating Polyominoes with Fixed Perimeter Defect

Andrei Asinowski, Gill Barequet, Yufei Zheng

Computer Science

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

A polyomino is an edge-connected set of cells on Z². To-date, no formulae enumerating polyominoes by area (number of cells) or perimeter (number of empty cells neighboring the polyomino) are known. We present a few formulae enumerating polyominoes with a fixed deviation from the maximum possible perimeter.

Original language	English
Pages (from-to)	61-67
Number of pages	7
Journal	Electronic Notes in Discrete Mathematics
Volume	61
DOIs	https://doi.org/10.1016/j.endm.2017.06.021
State	Published - Aug 2017

Keywords

Polyominoes
generating functions
linear recurrence

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

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https://doi.org/10.1016/j.endm.2017.06.021

Cite this

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title = "Enumerating Polyominoes with Fixed Perimeter Defect",

abstract = "A polyomino is an edge-connected set of cells on Z2. To-date, no formulae enumerating polyominoes by area (number of cells) or perimeter (number of empty cells neighboring the polyomino) are known. We present a few formulae enumerating polyominoes with a fixed deviation from the maximum possible perimeter.",

keywords = "Polyominoes, generating functions, linear recurrence",

author = "Andrei Asinowski and Gill Barequet and Yufei Zheng",

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year = "2017",

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doi = "https://doi.org/10.1016/j.endm.2017.06.021",

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AU - Asinowski, Andrei

AU - Barequet, Gill

AU - Zheng, Yufei

PY - 2017/8

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N2 - A polyomino is an edge-connected set of cells on Z2. To-date, no formulae enumerating polyominoes by area (number of cells) or perimeter (number of empty cells neighboring the polyomino) are known. We present a few formulae enumerating polyominoes with a fixed deviation from the maximum possible perimeter.

AB - A polyomino is an edge-connected set of cells on Z2. To-date, no formulae enumerating polyominoes by area (number of cells) or perimeter (number of empty cells neighboring the polyomino) are known. We present a few formulae enumerating polyominoes with a fixed deviation from the maximum possible perimeter.

KW - Polyominoes

KW - generating functions

KW - linear recurrence

UR - http://www.scopus.com/inward/record.url?scp=85026784955&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.endm.2017.06.021

DO - https://doi.org/10.1016/j.endm.2017.06.021

M3 - مقالة

SN - 1571-0653

VL - 61

SP - 61

EP - 67

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

Enumerating Polyominoes with Fixed Perimeter Defect

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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