Decorating Regular Tiles with Arcs

Year: 2011 Authors: David A. Reimann

Core claim

For a regular polygon with evenly divided sides, the number of arc-decorated tiles is enumerated by chord-diagram counts, with a separate Catalan count for noncrossing patterns.

Topics

tiling patterns, chord diagrams, crossing-free arcs, symmetry classes, Truchet tiles

Domains

combinatorics, enumeration, Catalan numbers, graphical pairing, tilings, pattern design, decorative tilings, Truchet-style motifs

Methods

endpoint numbering, combinatorial counting, recursive noncrossing test, symmetry classification, table-based enumeration

Media

regular polygon tiles, arcs, Bézier curves, chord diagrams

Source status

This page publishes metadata and extracted analytical signals only. Raw PDF and full OCR text are kept local for now.