Finding a Bijection Between the Kekulé Structures of Benzenoids and Weakly Increasing Matrices

Overview

Benzenoids are organic compounds composed of hexagonal six-carbon benzene rings with no adjacent double bonds. A Kekulé structure models a benzenoid as a collection of selected edges (representing double bonds) such that every vertex (representing a carbon atom) is paired with exactly one other vertex. Weakly increasing matrices are matrices whose entries are non-decreasing along every row and column. This research establishes a bijection between the set of Kekulé structures for certain hexagonal benzenoids and the set of two-row weakly increasing matrices with bounded integer entries. This bijection admits a geometrically intuitive interpretation and yields a compact encoding of these benzenoids. More broadly, this matrix-based perspective may open new directions in computational chemistry including faster simulations, improved representations for machine learning, and new approaches to molecular design.

Awards (2)

• American Mathematical Society: One-Year Membership to American Mathematical Society to each winner (7 winning projects, up to 3 team members per project)
• American Mathematical Society: Second Award of $1,000 $1,000

Competition history

• ISEF 2026 Mathematics · Entry MATH024

Resources

• ISEF abstract page ↗

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