references.md

layout	page
title	Project references
permalink	/references/
page_class	reference
description	Primary papers and authoritative references used by Tiling Foundry.
section	Yang–Zhang reduction
document_kind	Reference bibliography
status	Current reference policy
updated	2026-08-21
nav_order	30

Project references

This file records the primary external sources used by the project and where their authoritative copies can be obtained. It intentionally links to papers instead of vendoring their PDFs when the published license does not explicitly permit third-party redistribution.

License status was checked on 11 August 2026. This is a conservative repository policy, not legal advice.

Fixed Wang tiles and finite-region reduction

Chao Yang and Zhujun Zhang, NP-completeness of Tiling Finite Simply Connected Regions with a Fixed Set of Wang Tiles, arXiv:2405.01017v2, 2024.

• arXiv record and PDF
• DOI
• Repository status: link only. The selected arXiv license grants arXiv a non-exclusive right to distribute; it does not itself grant this repository a redistribution license.

This is the primary source for the fixed set of 23 Wang tiles, the 14 generalized tiles, and the Cubic Monotone 1-in-3 SAT reduction implemented by the project.

Earlier simply-connected rectangle construction

Igor Pak and Jed Yang, Tiling Simply Connected Regions with Rectangles, Journal of Combinatorial Theory, Series A 120(7), 1804--1816, 2013.

• arXiv record and PDF
• Publisher DOI
• Author-hosted copy
• Repository status: link only. The arXiv submission uses the same non-exclusive distribution license, and no separate redistribution license was found on the author-hosted copy.

This is the earlier fixed-rectangle NP-completeness result improved by the Yang–Zhang construction.

Wang tiles, computation, and the square-to-hex motivation

Sky Basire, Wang Tiles, University of Canterbury summer project report, 2022.

• Institutional repository record
• DOI
• Repository status: link only. The institutional record explicitly labels the report All Rights Reserved.

The report provides an accessible overview of the Domino Problem, computation with Wang tiles, and examples of square-to-hex Wang-tile constructions.

Policy for adding local copies

A PDF may be added under docs/papers/ only when at least one of the following is recorded alongside it:

• an explicit Creative Commons or equivalent redistribution license covering that version;
• written permission from the copyright holder to redistribute it in this repository;
• a public-domain statement applicable to the work.

The local entry should preserve attribution, source URL, exact version, license text or permission record, and the date it was retrieved. Free access or an author-hosted download link alone is not treated as redistribution permission.