The O-Sequence:Representation of 3D-Dissection

Hidenori OHTA
Toshinori YAMADA
Chikaaki KODAMA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A    No.8    pp.2111-2119
Publication Date: 2008/08/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.8.2111
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Algorithms and Data Structures
rectangular solid dissection,  rectangular dissection,  3D-VLSI,  2D-dissection,  3D-dissection,  Q-sequence,  O-sequence,  

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A 3D-dissection (A rectangular solid dissection) is a dissection of a rectangular solid into smaller rectangular solids by planes. In this paper, we propose an O-sequence, a string of representing any 3D-dissection which is dissected by only non-crossing rectangular planes. We also present a necessary and sufficient condition for a given string to be an O-sequence.