Combinatorics, Lecture 5 (10 October 2019)

Thanks to Tim Hosgood for helping me type these notes up. Previous lecture here. Fibonacci and `tribonacci' numbers Recall: there's a species $latex G \colon \mathsf S \to \mathsf F$ with G(X) = {ways to totally order X and chop it into blocks of length 1 or 2} For example, We saw that $latex |G|(X) … Continue reading Combinatorics, Lecture 5 (10 October 2019)

Combinatorics, Lecture 4 (8 Oct 2019)

Lecture 3 here. Using Generating Functions We defined two binary operations on species $latex \mathsf{S} \to \mathsf{Set}$: Addition. $latex (G+H)(X)=G(X)+H(X)$; Multiplication. $latex (GH)(X) = \{(Y,g,h) \mid Y \subseteq X, g \in G(Y), h \in H (X \setminus Y)\}$. These obey $latex |G+H| = |G|+|H|$ and $latex |GH|=|G||H|$. In total, we'll talk about five binary operations … Continue reading Combinatorics, Lecture 4 (8 Oct 2019)