#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:

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

#Attendance Question
#Use Lagrange inversion formula to find an explicit expression for the 
#coeff 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
#Attendance Answer
#i (1/n)*(1+u(x))^2
#ii (1/n)*(1+u(x))^3
#iii (1/n)*(1+u(x))^3

#Attendance Question
#RandF(16);
#[13,7,15,10,13,16,6,2,11,12,4,6,5,11,16,1]
#F(1)=13,f(2)=7,....f(16)=1
#i) Draw this directed graph
#       8-2-7-6-16-15-3-1-13-5 
#             |
#   9-11-4-10-12
#      |
#     14
#Find the Doubly-rooted tree that is outputted by the royal bijections 
#{{1,13},{1,16},{2,7{,{2,8},{3,15},{4,11},{5,13},{6,7},{6,12},{6,16},{9,11},{10,12},{11,14},{15,16},{13,5}}

#Attendance Question
Finish this Find the pruffer code (of length 11) of the original tree
#Attendance Answer
#[13,7,15,10,13,16,6,2,11,12,4,6,5,11,16,1]