Welcome to Week 2 of "Analytic Combinatorics."
This week, we address the idea of using multivariate generating
functions to study combinatorial parameters, such as leaves in trees
or cycles in permutations.
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Lecture 3: Combinatorial Parameters and MGFs. This lecture describes
the process of adding variables to mark parameters and then using the
constructions form Lectures 1 and 2 and natural extensions of the
transfer theorems to define multivariate GFs that contain information
about parameters. We concentrate on bivariate generating functions
(BGFs), where one variable marks the size of an object and the other
marks the value of a parameter. After studying ways of computing the
mean, standard deviation and other moments from BGFs, we consider
several examples in some detail.
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Your assignment for this week, due at 11:59PM on
Thursday, March 31, 2022
is to write up and submit solutions to
Note III.17 and Web Exercise III.3 on the "Analytic
Combinatorics" booksite. Please note that "Notes" in the book are
often written as statements instead of questions, so the versions on
the booksite are slightly reworded to clarify what you need to do.
As usual, submit a potential exam question on the week's material.
Submit files named
"AC2-Q1.pdf"
"AC2-Q2.pdf"
"AC2-QQ.pdf"
via codePost.
RS