https://peertube.wtf/videos/watch/e37d9212-c9f3-4b11-81a3-559568ee6cdd This is a talk that I gave for the University of Denver Algebra and Logic Seminar in the fall of 2023. I discuss a formula I found when I was a graduate student which involves the partition numbers. During the summer of 2023 I was reminded of this and posted a preprint to the arXiv (linked below) which I mostly wrote back then. The formula is obtained by using Burnside's Lemma in the context of monoid representations on a finite set. Title: Monoid representations and partitions Abstract: When I began graduate school, I was interested in the representation theory of monoids, so I studied the set representations of the free idempotent monoid on one generator. These are nothing more than the idempotent maps from the set to itself. The collection of such maps carries a natural group action. By applying Burnside's Lemma this leads to a formula which only involves a partition number and elementary functions. One side involves a summation over a set closely related to the partition number, however. Some speculation is made as to how to eliminate this summation. Slides: https://aten.cool/documents/slides/aten_du_algebra_logic_2023.pdf Paper: https://aten.cool/documents/papers/idempotents2023.pdf Tue, 18 Aug 2026 12:33:56 GMT https://validator.w3.org/feed/docs/rss2.html PeerTube - https://peertube.wtf https://peertube.wtf/lazy-static/avatars/45856119-df14-4b5f-bff8-4807ae2cfbd2.png https://peertube.wtf/videos/watch/e37d9212-c9f3-4b11-81a3-559568ee6cdd All rights reserved, unless otherwise specified in the terms specified at https://peertube.wtf/about and potential licenses granted by each content's rightholder.