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Presentations of diagram categories

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arxiv 1910.11784 v2 pith:XRAORXRS submitted 2019-10-25 math.RT math.CT

Mengwei Hu This is my paper · ORCID
classification math.RTmath.CT
keywords categorydiagramsrookcategoriesmotzkinplanarrook-brauerbases
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We describe the planar rook category, the rook category, the rook-Brauer category, and the Motzkin category in terms of generators and relations. We show that the morphism spaces of these categories have linear bases given by planar rook diagrams, rook diagrams, rook-Brauer diagrams, and Motzkin diagrams.

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  1. Representation gaps of rigid planar diagram monoids

    math.RT 2025-05 conditional novelty 6.0 of 10

    Rigid non-pivotal Temperley-Lieb, Motzkin, and planar rook monoids have smaller representation gaps than their pivotal counterparts, making them worse for cryptographic use.

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