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arXiv · 2303.04531

Restricted Partitions and $SL_2$ Cohomology

Steven Benzel·Scott Conner·Nham Ngo·Khang Pham
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Abstract

The aim of this paper is twofold. First, we study the number of partitions of a positive integer $m$ into at most $n$ parts in a given set $A$. We prove that such a number is bounded by the $n$-th Fibonacci number $F(n)$ for any $m$ and some family of sets $A$ including sets of powers of an integer. Then, in the second part of the paper, we provide new results in bounding the cohomology of the simple algebraic group $SL_2$ with coefficients in Weyl modules.

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BibTeXRIS

Steven Benzel, Scott Conner, Nham Ngo, Khang Pham. 2023-03-08. Restricted Partitions and $SL_2$ Cohomology. https://arxiv.org/abs/2303.04531

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