Representation gaps of rigid planar diagram monoids
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912367444492288 |
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| author | Stewart, Willow Tubbenhauer, Daniel |
| author_facet | Stewart, Willow Tubbenhauer, Daniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05846 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representation gaps of rigid planar diagram monoids Stewart, Willow Tubbenhauer, Daniel Representation Theory Cryptography and Security Group Theory Quantum Algebra Primary: 18D10, 20M30, Secondary: 05A16, 94A60 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. |
| title | Representation gaps of rigid planar diagram monoids |
| topic | Representation Theory Cryptography and Security Group Theory Quantum Algebra Primary: 18D10, 20M30, Secondary: 05A16, 94A60 |
| url | https://arxiv.org/abs/2505.05846 |