arXiv subjects

Willow Stewart

Publications and source records attributed to Willow Stewart.

2 recordsLinked to original sources

arXiv2025

Generalized diagram categories and monoids, and their representations

Classical diagram categories and monoids, including the Temperley--Lieb, Brauer, and partition cases, arise as special instances of the category of two dimensional cobordisms and admit additional twists that produce a large new family of diagram categories and monoids. In this paper we introduce this family and develop a unified approach to their representation theory.

math.RT↗

arXiv2025

Representation gaps of rigid planar diagram monoids

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.

math.RT↗