#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 positive integer k, u(x) = x*(1+u(x))^k

2. Let F:=[13,7,15,10,13,16,6,2,11,12,4,6,5,11,16,1].
i) Draw the directed graph
Find the doubly-rooted tree that is outputted by the Joyal Bijection.
Check that it is as below

3. Finish this. Find the Pruffer code (of length 11) of the original tree.
2,4,11,10,3,6,2,3,6,7,8