Star Anagram Detection and Classification

TL;DR

This paper introduces automated detection and classification methods for star anagrams, explores their mathematical properties, and provides an extensive analysis of their occurrence and shapes in English words.

Contribution

It presents novel algorithms for identifying star anagrams and classifying their symmetries, along with mathematical proofs and a comprehensive English word analysis.

Findings

Star anagrams are rare, constituting about 5.7% of English anagrams.

Maximally symmetric star anagrams exhibit specific properties linked to modular arithmetic.

Numerical analysis reveals clustering patterns and notable geometric shapes among English star anagrams.

Abstract

A star anagram is a rearrangement of the letters of one word to produce another word where no letter retains its original neighbors. These maximally shuffled anagrams are rare, comprising only about 5.7% of anagrams in English. They can also be depicted as unicursal polygons with varying forms, including the eponymous stars. We develop automated methods for detecting stars among other anagrams and for classifying them based on their polygon's degree of both rotational and reflective symmetry. Next, we explore several properties of star anagrams including proofs for two results about the edge lengths of perfect, i.e., maximally symmetric, stars leveraging perhaps surprising connections to modular arithmetic and the celebrated Chinese Remainder Theorem. Finally, we conduct an exhaustive search of English for star anagrams and provide numerical results about their clustering into common shapes along with examples of geometrically noteworthy stars.