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arXiv · 2505.05846

Representation gaps of rigid planar diagram monoids

Willow Stewart·Daniel Tubbenhauer
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Abstract

We define non-pivotal analogs of the Temperley-Lieb, Motzkin, and planar rook monoids, and compute bounds for the sizes of their nontrivial simple representations. From this, we assess the two types of monoids in their relative suitability for use in cryptography by comparing their representation gaps and gap ratios. We conclude that the non-pivotal monoids are generally worse for cryptographic purposes.

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Willow Stewart, Daniel Tubbenhauer. 2025-05-09. Representation gaps of rigid planar diagram monoids. https://arxiv.org/abs/2505.05846

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