Kenneth Chan
#ATTENDANCE QUIZ FOR LECTURE 14 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p14
#with an attachment called
#p14FirstLast.txt
#(e.g. p14DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Oct. 24, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE:

PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH, BY THE ANSWER
Attendance Problem 1
Where and when was Herbert S. Wilf born?
Look up his paper about "random generation of combinatorial objects"
Advances in Mathematics ca. 1980 and at least skim it.
Answer
Dob June 13 1931
Born Philadelphia

Attendance Problem 2
Let m:=Age of Donald Trump
n:=Age of Joe Biden
What is the probability that if you take a random lattice walk from [0,0] to 
[n,m] you will always stay in the region x>=y
Answer
Trump-74
Biden-77
.48951...

Attendance Problem 3
What is a Wilf-ZeilBerger Pair
Answer
A pair of functions that can be used to certify certain combinatorcial identities 

Attendance Problem 4
What nationality was Catalan? What is the constant named after him?
Answer
Belgian French
Constant equal exactly to pi^3/32

Attendance Problem 5
Do the same for [1,1,-1,-1,1] and get a set of 10 such lists that
is the whole of paths(3,2);
Answer
[-1,-1,1,1,1],[-1,1,-1,1,1],[-1,1,1,-1,1],[-1,1,1,1,-1],[1,-1,-1,1,],[1,-1,1,-1,1],[1,-1,1,1-1],
[1,1,-1,-1,1],[1,1,-1,1,-1],[1,1,1,-1,-1]

Attendance probelm 6
You are in a circular track in the desert. At random places there are gas containers with random amounts of gas
a1,a2,..., ak gallons are exactly what you need to drive in this track 
Prove that there exists a location on the circular track such that you start there 
you dont run out of gas 
Decive a method for doing it
Answer
Suppose that can1 has enough enough gas enable to make it to can 2.
this implies that k will possible have enough for k+1.
Leading to the idea that k can possiblility lead to infinite k+1s.