Minimum transformation representations of diagram monoids
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915798874849280 |
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| author | Cirpons, Reinis East, James Mitchell, James D. |
| author_facet | Cirpons, Reinis East, James Mitchell, James D. |
| contents | We obtain formulae for the minimum transformation degrees of the most well-studied families of finite diagram monoids, including the partition, Brauer, Temperley--Lieb and Motzkin monoids. For example, the partition monoid $P_n$ has degree $1 + \frac{B(n+2)-B(n+1)+B(n)}2$ for $n\geq2$, where these are Bell numbers. The proofs involve constructing explicit faithful representations of the minimum degree, many of which can be realised as (partial) actions on projections. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_14693 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimum transformation representations of diagram monoids Cirpons, Reinis East, James Mitchell, James D. Rings and Algebras Combinatorics We obtain formulae for the minimum transformation degrees of the most well-studied families of finite diagram monoids, including the partition, Brauer, Temperley--Lieb and Motzkin monoids. For example, the partition monoid $P_n$ has degree $1 + \frac{B(n+2)-B(n+1)+B(n)}2$ for $n\geq2$, where these are Bell numbers. The proofs involve constructing explicit faithful representations of the minimum degree, many of which can be realised as (partial) actions on projections. |
| title | Minimum transformation representations of diagram monoids |
| topic | Rings and Algebras Combinatorics |
| url | https://arxiv.org/abs/2411.14693 |