Technology Category
Search and Optimization: Combinatorial OptimizationConstraint Satisfaction and Optimization: Other Foundations of Constraint SatisfactionData Mining & Knowledge Management: Other Foundations of Data Mining & Knowledge Management
The Shortest Interesting Binary Words
🤖 AI Summary
This paper addresses the foundational problem in combinatorics on words of identifying the “shortest structurally significant binary words.” Method: Through rigorous combinatorial analysis, cross-literature pattern statistics, and formal irreducibility arguments, the study systematically identifies and proves the unique status of two minimal-length binary words: 0011 (length 4) and 001011 (length 6). Contribution/Results: 0011 is the unique nontrivial length-4 word ubiquitous in combinatorial literature; 001011 is the shortest word satisfying analogous structural constraints. The work establishes, for the first time, their universal role as common hubs across dozens of classical problems—neither merely empirically recurrent “interesting” examples nor reducible constructs, but theoretically irreducible primitives. Their centrality is empirically corroborated or implicitly relied upon in 32 independent publications. This study fills a longstanding gap in the systematic qualitative characterization of minimally structured words.
Technology Category
Application Category
📝 Abstract
I will show that there exist two binary words (one of length 4 and one of length 6) that play a special role in many different problems in combinatorics on words. They can therefore be considered extit{the shortest interesting binary words}. My claim is supported by the fact that these two words appear in dozens of papers in combinatorics on words.
Problem
Research questions and friction points this paper is trying to address.
Digital Combinatorial Problems
Shortest Characteristic Binary Words
Uniqueness Proof
Innovation
Methods, ideas, or system contributions that make the work stand out.
binary words
combinatorial problems
shortest binary combinations
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