Q1. THE FIRST ATTENDANCE QUESTION WAS:
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 integers
u(x)=x*(1+u(x))^k

A1. MY ANSWER TO THE FIRST ATTENDANCE QUESTION IS:



Q2. THE  SECOND ATTENDANCE QUESTION WAS:
Consider the fucntion f(1)=13, f(2)=7,..f(16)=1
i. draw the directed graph
find the doubly rooted tree that is outputted by the joyal bijection
check it is as below

A2. MY ANSWER TO THE  SECOND ATTENDANCE QUESTION IS:



Q3. THE  THIRD ATTENDANCE QUESTION WAS:
Finish this and find the pruffer code of the original tree

A3. MY ANSWER TO THE  THIRD ATTENDANCE QUESTION IS:



Q4. THE  FOURTH ATTENDANCE QUESTION WAS:


A4. MY ANSWER TO THE  FOURTH ATTENDANCE QUESTION IS:



Q5. THE  FIFTH ATTENDANCE QUESTION WAS:


A5. MY ANSWER TO THE  FIFTH ATTENDANCE QUESTION IS:



Q6. THE  SIXTH ATTENDANCE QUESTION WAS


A6. MY ANSWER TO THE  SIXTH ATTENDANCE QUESTION IS



Q7. THE  SEVENTH ATTENDANCE QUESTION WAS


A7. MY ANSWER TO THE  SEVENTH ATTENDANCE QUESTION IS



Q8. THE  EIGHTH ATTENDANCE QUESTION WAS


A8. MY ANSWER TO THE  EIGHTH ATTENDANCE QUESTION IS