Restricted Partitions and $SL_2$ Cohomology

Steven Benzel; Scott Conner; Nham Ngo; Khang Pham

Restricted Partitions and $SL_2$ Cohomology

Representation Theory 2023-11-09 v2 Combinatorics Number Theory

Authors: Steven Benzel , Scott Conner , Nham Ngo , Khang Pham

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.

Keywords

integer partitions fibonacci numbers sl2 cohomology weyl modules algebraic groups

Cite

@article{arxiv.2303.04531,
  title  = {Restricted Partitions and $SL_2$ Cohomology},
  author = {Steven Benzel and Scott Conner and Nham Ngo and Khang Pham},
  journal= {arXiv preprint arXiv:2303.04531},
  year   = {2023}
}

Comments

to appear in the Albanian Journal of Mathematics

Restricted Partitions and $SL_2$ Cohomology

Abstract

Keywords

Cite

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