First I’ll state the Cycle Length Lemma, which summarizes a lot of interesting facts about random permutations. Then I’ll state and prove a categorified version of the Cycle Length Lemma, which ...

In combinatorics, permutations are important objects with many operations. In this paper, we define a coupling product on permutations and prove that the space spanned by permutations is a graded ...

Now six full match weeks into the new UEFA Champions League format, the table has been flushed out to show where each side stands amongst their peers across the European continent. Thanks to the ...

Technically, a solar generator doesn’t actually generate solar power that you can use unless you have both. What’s more, most of these generators are large enough that it isn’t really ...