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Logical Matrix Representations in Map Folding

Yiyang JIA, Jun MITANI, Ryuhei UEHARA

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Summary :

Logical matrices are binary matrices often used to represent relations. In the map folding problem, each folded state corresponds to a unique partial order on the set of squares and thus could be described with a logical matrix. The logical matrix representation is powerful than graphs or other common representations considering its association with category theory and homology theory and its generalizability to solve other computational problems. On the application level, such representations allow us to recognize map folding intuitively. For example, we can give a precise mathematical description of a folding process using logical matrices so as to solve problems like how to represent the up-and-down relations between all the layers according to their adjacency in a flat-folded state, how to check self-penetration, and how to deduce a folding process from a given order of squares that is supposed to represent a folded state of the map in a mathematical and natural manner. In this paper, we give solutions to these problems and analyze their computational complexity.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.10 pp.1401-1412
Publication Date
2022/10/01
Publicized
2022/03/24
Online ISSN
1745-1337
DOI
10.1587/transfun.2021EAP1165
Type of Manuscript
PAPER
Category
Mathematical Systems Science

Authors

Yiyang JIA
  Seikei University
Jun MITANI
  University of Tsukuba
Ryuhei UEHARA
  JAIST

Keyword