Hamiltonian paths on directed grids
Mih\'aly Hujter, Andr\'as Kaszanyitzky
TL;DR
This paper explores Hamiltonian paths on directed grids related to recursive FASS-curves, providing formulas connected to Fibonacci numbers and domino tilings, with implications for geometric constructability.
Contribution
It introduces a new class of Hamiltonian paths on directed grids linked to recursive curves and establishes formulas related to Fibonacci numbers and domino tilings.
Findings
Derived formulas for counting Hamiltonian paths.
Established connections to Fibonacci numbers and domino tilings.
Discussed implications for geometric constructability.
Abstract
Our studies are related to a special class of FASS-curves, which can be described in a node-rewriting Lindenmayer-system. These ortho-tile (or diagonal) type recursive curves inducing Hamiltonian paths. We define a special directed graph on a rectangular grid, and we enumerate all Hamiltonian paths on this graph. Our formulas are strongly related to both the Fibonacci numbers and the domino tilings of chessboards. The constructability of the regular -gon with straightedge and compass is also related.
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Taxonomy
TopicsCellular Automata and Applications · Algorithms and Data Compression · Topological and Geometric Data Analysis