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<p>Using grid diagrams, we establish a methodology to encode and analyze pretzel links, enabling a systematic approach of their topological and algebraic properties. By employing a combination of knot theory, graph theory, and combinatorial techniques, we uncover relationships between the structure of pretzel links and their corresponding grid diagram representations. Additionally, we present computational techniques for efficiently generating and analyzing invariants of these specific grid diagrams. Within this paper, we provide the reader with an expository overview of grid diagrams and pretzel links, provide theorems and conjectures about combinatorial properties of the pretzel links’ grid diagrams, and supply the reader future directions for study and research.</p>

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Exploring the combinatorics of pretzel links through grid diagrams

  • 期刊论文

  • 发表日期：

    2025年3月27日

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  • Janee Schrader,
  • Carolyn Otto

摘要

Using grid diagrams, we establish a methodology to encode and analyze pretzel links, enabling a systematic approach of their topological and algebraic properties. By employing a combination of knot theory, graph theory, and combinatorial techniques, we uncover relationships between the structure of pretzel links and their corresponding grid diagram representations. Additionally, we present computational techniques for efficiently generating and analyzing invariants of these specific grid diagrams. Within this paper, we provide the reader with an expository overview of grid diagrams and pretzel links, provide theorems and conjectures about combinatorial properties of the pretzel links’ grid diagrams, and supply the reader future directions for study and research.