2 problems

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The rank bounds conjecture for $\Sigma_n^4$ and $\Sigma_n^5$
Rank bounds conjecture. One might conjecture that
Conjectureopencombinatorics permutation-groups transformation-monoidsarXiv posted 2 days ago
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Ponizovskiĭ's finite representation type conjecture for full transformation monoids
Let $\mathfrak T_n$ be the monoid of all self-maps of an $n$ -element set, and let $\mathbb C\mathfrak T_n$ be its complex monoid algebra. A finite-dimensional algebra has finite re…
Conjectureopenfinite-dimensional-algebras representation-theory transformation-monoidsarXiv posted 2 days ago

The rank bounds conjecture for Σn4\Sigma_n^4Σn4​ and Σn5\Sigma_n^5Σn5​