#ATTENDANCE QUIZ FOR LECTURE 23 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p23
#with an attachment called
#p23FirstLast.txt
#(e.g. p23DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Dec. 4, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE: 3

PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH, BY THE ANSWER

1. Use Lagrange inversion formula to find an explicit expression for the coefficient of x^n in the power series of u(x) that satisfies the functional equations
(i) u(x)=x*(1+u(x))^2
(ii) u(x)=x*(1+u(x))^3
(iii) for any k, pos integer 
u(x)=x*(1+u(x))^k

2. Consider the function Given above
f(x)=13, f(x)=7,...f(16)=1
(i) Draw this directed graph
Find the doubly-rooted tree that is outputted by the joyal bijection

3. Finish this. Find the Pruffer code (of length 11) of the original tree.
[10, 1, 3, 5, 3, 1, 5, 10, 10]