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


2. Consider the function above. 
(i) Draw this directed graph 
(ii) 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. 
InvPruffer([2,4,11])